A2 Physics. Unit 5. Unit 4. Fields and Further Mechanics. Nuclear and Thermal Physics. 1 Momentum and Collisions. 1 Rutherford Scattering

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1 A Physics Unit 4 Fields and Futhe Mechanics Momentum and Collisions Foce and Impulse Cicula Motion 4 Centipetal Foce and Acceleation 5 Simple Hamonic Motion 6 SHM Gaphs 7 SHM Time Peiods 8 Resonance and Damping 9 Gavitational Fields Gavitational Potential Obits and Escape Velocity Electic Fields Electic Potential 4 Fields Compaison Unit 5 Nuclea and Themal Physics Ruthefod Scatteing Ionising Radiation Radioactive Decay 4 Modes of Decay 5 Nuclea Radius 6 Mass and Enegy 7 Fission and Fusion 8 Nuclea Reactos 9 Nuclea Safety Aspects Heat, Tempeatue and Intenal Enegy The Specifics Gas Laws Ideal Gas 4 Molecula Kinetic Theoy Model 5 Capacitos 6 Chaging and Dischaging 7 Exponential Decay 8 Foce on a Cuent Caying Wie 9 Foce on a Chaged Paticle Magnetic Flux and Flux Linkage Electomagnetic Induction Tansfomes

2 Lesson Leaning Momentum and Collisions To be able to calculate momentum and know the units To be able to explain the diffeence between elastic and inelastic collisions To be able to find the velocity of an object afte a collision o explosion Momentum (Also seen in GCSE Physics ) The momentum of an object is given by the equation: momentum = mass x velocity p mv Since it depends on the velocity and not speed, momentum is a vecto quantity. If we assign a diection to be positive fo example if was positive, an object with negative velocity would be moving. It would also have a negative momentum. Momentum is measued in kilogam metes pe second, kg m/s o kg m s - Consevation (Also seen in GCSE Physics ) In an isolated system (if no extenal foces ae acting) the linea momentum is conseved. We can say that: the total momentum befoe = the total momentum afte The total momentum befoe and afte what? A collision o an explosion. Collisions (Also seen in GCSE Physics ) Thee ae two types of collisions; in both cases the momentum is conseved. Elastic kinetic enegy in conseved, no enegy is tansfeed to the suoundings If a ball is dopped, hits the floo and bounces back to the same height it would be an elastic collision with the floo. The kinetic enegy befoe the collision is the same as the kinetic enegy afte the collision. Inelastic kinetic enegy is not conseved, enegy is tansfeed to the suoundings If a ball is dopped, hits the floo and bounces back to a lowe height than eleased it would be an inelastic collision. The kinetic enegy befoe the collision would be geate than the kinetic enegy afte the collision. Befoe Afte In the situation above, ca and ca tavel to the ight with initial velocities u and u espectively. Ca catches up to ca and they collide. Afte the collision the cas continue to move to the ight but ca now tavels at velocity v and ca tavels a velocity v. [ is positive] Since momentum is conseved the total momentum befoe the cash = the total momentum afte the cash. The total momentum befoe is the momentum of A + the momentum of B The total momentum afte is the new momentum of A + the new momentum of B We can epesent this with the equation: mu mu mv mv Explosions (Also seen in GCSE Physics ) We look at explosions in the same way as we look at collisions, the total momentum befoe is equal to the total momentum afte. In explosions the total momentum befoe is zeo. [ is positive] Befoe Afte If we look at the example above we can see that the whole system is not moving, so the momentum befoe is zeo. Afte the explosion the shell tavels ight with velocity v and the cannon ecoils with a velocity v. The momentum of the system is given as: mu mu mv mv So the equation fo this diagam would be: mv mv But emembe, v is negative so: mv mv mv mv

3 Lesson Leaning Foce and Impulse To be able to calculate foce fom change in momentum To be able to explain and calculate impulse To know the significance of the aea unde a foce-time gaph Foce (Also seen in GCSE Physics ) If we stat at F = ma we can deive an equation that links foce and momentum. ( v u) F ma we can eplace a in this equation with a fom Unit t ( v u) F m multiplying out makes the equation t mv mu ( mv) F o F whee means the change in t t This states that the foce is a measue of change of momentum with espect to time. This is Newton s Second Law of Motion: The ate of change of an object s linea momentum is diectly popotional to the esultant extenal foce. The change in the momentum takes place in the diection of the foce. If we have a tolley and we incease its velocity fom est to m/s in seconds, we know that it takes a bigge foce to do the same with a tolley that s full of shopping. Eve tied tuning a tolley aound a cone when empty and then when full? Foce is measued in Newtons, N Ca Safety (Also seen in GCSE Physics ) Many of the safety featues of a ca ely on the above equation. Aibags, seatbelts and the cumple zone incease the time taken fo the ca and the people inside to stop moving. Inceasing the time taken to change the momentum to zeo educes the foce expeienced. Catching An Egg: If we held ou hand out and didn t move it the egg would smash. The change in momentum happens in a shot time, making the foce lage. If we cup the egg and move ou hands down as we catch it we make it take longe to come to a complete stop. Inceasing the time taken deceases the foce and the egg emains intact. Cicket Ball: If we didn t move ou hands it would hut when the ball stopped in ou hands. If we make it take longe to stop we educe the foce on ou hands fom the ball. Impulse mv mu F t multiply both sides by t Ft mv mu ( mv) F t multiply both sides by t F t (mv) We now have an equation fo impulse. Impulse is the poduct of the foce and the time it is applied fo. An impulse causes a change in momentum. Impulse is measued in Newton seconds, Ns Since F t (mv), the same impulse (same foce applied fo the same amount of time) can be applied to a small mass to cause a lage velocity o to a lage mass to cause a small velocity Ft = mv = mv Foce-Time Gaphs The impulse can be calculated fom a foce-time gaph, it is the same as the aea unde the gaph. The aea of the fist gaph is given by: height x length = Foce x time = Impulse

4 Lesson Leaning Cicula Motion To be able to calculate the angula displacement of an object moving in a cicle To be able to calculate the angula speed of an object moving in a cicle To be able to calculate the speed of an object moving in a cicle To the ight is the path a ca is taking as it moves in a cicle of adius. Angula Displacement, θ As the ca tavels fom X to Y it has tavelled a distance of s and has coveed a section of the complete cicle it will make. It has coveed and angle of θ which is called the angula displacement. ac adius s Radians adian is the angle made when the ac of a cicle is equal to the adius. ac Fo a complete cicle adius A complete cicle is 6 so Angula Speed, ω cicumfeence adius 6 = π ad =.7 ad 57. = ad Angula Displacement is measued in adians, ad Angula speed is the ate of change of angula displacement, o the angle that is coveed evey second. t Angula Speed is measued in adians pe second, ad/s o ad s - Fequency, f Fequency is the numbe of complete cicles that occu evey second. Fo one cicle;, if we substitute this into the equation above we get t This equation says that the angula speed (angle made pe second) is equal to one cicle divided by the time taken to do it. Vey simila to speed = distance/time Since f the above equation can be witten as f T Fequency is measues in Hetz, Hz Speed, v The velocity of the ca is constantly changing because the diection is constantly changing. The speed howeve, is constant and can be calculated. s v If we eaange the top equation we can get s, the speed then becomes t v Now if we eaange the second equation we get t, the equation becomes t t v Cancel the t s and we finally aive at ou equation fo the speed. t v Speed is measued in metes pe second, m/s o m s -

5 Lesson 4 Leaning Centipetal Foce and Acceleation To be able to calculate the centipetal acceleation of an object moving in a cicle To be able to calculate the centipetal foce that keeps an object moving in a cicle To be able to explain why the centifugal foce does not exist Moving in a Cicle (Also seen in GCSE Physics ) Fo an object to continue to move in a cicle a foce is needed that acts on the object towads the cente of the cicle. This is called the centipetal foce and is povided by a numbe of things: Fo a satellite obiting the Eath it is povided by gavitational attaction. Fo a ca diving aound a oundabout it is povided by the fiction between the wheels and the oad. Fo a ball on a sting being swung in a cicle it is povided by the tension in the sting. Centipetal foce acts fom the body to the cente of a cicle Since F=ma the object must acceleate in the same diection as the esultant foce. The object is constantly changing its diection towads the cente of the cicle. Centipetal acceleation has diection fom the body to the cente of the cicle Centifugal Foce Some people thought that an object moving in a cicle would expeience the centipetal foce acting fom the object towads the cente of the cicle and the centifugal foce acting fom the object away fom the cente of the cicle. They thought this because if you sit on a oundabout as it spins it feels like you ae being thown off backwads. If someone was watching fom the side they would see you ty and move in a staight line but be pulled in a cicle by the oundabout. The centifugal foce does not exist in these situations. Centipetal Acceleation The centipetal acceleation of an object can be deived if we look at the situation to the ight. An object of speed v makes an angula displacement of θ in time t. v a t If we look at the tiangle at the fa ight we can use s v when θ is small. This becomes: v We can eaange this to give: v v v Acceleation is given by a substitute the above equation into this one t v a this is the same as a v t t In lesson (Cicula Motion) we established that, substitute this into the equation above t a v If we use v we can deive two moe equations fo acceleation v a v a a Centipetal Acceleation is measued in metes pe second squaed, m/s o m s - Centipetal Foce We can deive thee equations fo the centipetal foce by using acceleation fom above. F mv F m F ma and the thee equations of v F m Centipetal Foce is measued in Newtons, N

6 Lesson 5 Leaning Simple Hamonic Motion To know what simple hamonic motion is To be able to descibe the acceleation of an SHM system To be able to calculate the displacement, velocity and acceleation of an SHM system Oscillations In each of the cases below thee is something that is oscillating, it vibates back and foth o up and down. Each of these systems is demonstating Simple Hamonic Motion (SHM). SHM Chaacteistics The equilibium point is whee the object comes to est, in the simple pendulum it at its lowest point. If we displace the object by a displacement of x thee will be a foce that bings the object back to the equilibium point. We call this the estoing foce and it always acts in the opposite diection to the displacement. We can epesent this as: F x Since F ma we can also wite: a x Fo an object to be moving with simple hamonic motion, its acceleation must satisfy two conditions: *The acceleation is popotional to the displacement *The acceleation is in the opposite diection to the displacement (towads the equilibium point) Equations The following equations ae tue fo all SHM systems but let us use the simple pendulum when thinking about them. The pendulum bob is displaced in the negative diection when at point, it is eleased and swings though point at its maximum speed until it eaches point whee it comes to a complete stop. It then swings to the negative diection, eaches a maximum speed at 4 and completes a full cycle when it stops at 5. Displacement, x The displacement of the bob afte a time t is given by the equation: Since f the equation can become: x Acos t T T (whee t is the time into the cycle and T is the time fo one complete cycle) The maximum displacement is called the amplitude, A. x Acos ft (CALCS IN RAD) t x Acos T x A MAXIMUM Velocity, v The velocity of the bob at a displacement of x is given by the equation: v f A x The maximum velocity occus in the middle of the swing ( and 4) when displacement is zeo (x = ) v f A x v f A v f A v fa MAXIMUM Acceleation, a The acceleation of the bob at a displacement of x is given by the equation: a ( f ) x As discussed befoe the acceleation acts in the opposite diection to the displacement. The maximum acceleation occus at the ends of the swing (, and 5) when the displacement is equal to the amplitude (x = A). a ( f ) x a ( f ) A MAXIMUM

7 Lesson 6 Leaning SHM Gaphs To be able to sketch the gaphs of displacement, velocity and acceleation fo a simple pendulum To be know what the gadients epesent To be able to explain the enegy in a full cycle and sketch the gaph Pendulum Conside the simple pendulum dawn below. When eleased fom A the bob acceleates and moves to the cente point. When it eached B it has eached a maximum velocity in the positive diection and then begins to slow down. At C it has stopped completely so the velocity is zeo, it is at a maximum displacement in the positive and acceleates in the negative diection. At D it is back to the cente point and moves at maximum velocity in the negative diection. By E the velocity has dopped to zeo, maximum negative displacement and a massive acceleation as it changes diection. This epeats as the pendulum swings though F, G, H and back to I. Below ae the gaphs that epesent this: Gadients s Since v the gadient of the displacement gaph gives us velocity. At C the gadient is zeo and we can see t that the velocity is zeo. v Also since a the gadient of the velocity gaph gives us acceleation. At C the gadient is a maximum in t the negative diection and we can see that the acceleation is a maximum in the negative diection. Enegy In all simple hamonic motion systems thee is a convesion between kinetic enegy and potential enegy. The total enegy of the system emains constant. (This is only tue fo isolated systems) Fo a simple pendulum thee is a tansfomation between kinetic enegy and gavitational potential enegy. At its lowest point it has minimum gavitational and maximum kinetic, at its highest point (when displacement is a maximum) it has no kinetic but a maximum gavitational. This is shown in the gaph. Fo a mass on a sping thee is a tansfomation between kinetic enegy, gavitational potential enegy and the enegy stoed in the sping (elastic potential). At the top thee is maximum elastic and gavitational but minimum kinetic. In the middle thee is maximum kinetic, minimum elastic but it still has some gavitational. At its lowest point it has no kinetic, minimum gavitational but maximum elastic.

8 Lesson 7 Leaning SHM Time Peiods To be able to calculate the time peiod of a simple pendulum To be able to calculate the time peiod of a mass on a sping To be able to descibe the expeiment to find g The Simple Pendulum In the diagam we can see that the estoing foce of the pendulum is: F mgsin x x When is less than (in adians) sin so the equation can become: F mg l l x Since both F ma and a ( f ) x (fo SHM) the equation now becomes: mg m( f ) x l g This simplifies to: ( f ) l Reaanging fo f gives us f g l And since f then: T T l g Time is measued in seconds, s Mass on a Sping When a sping with sping constant k and length l has a mass m attached to the bottom it extends by an extension e, this is called the static extension and is the new equilibium point. The tension in the sping is balanced by the weight. We can epesent this as: If the mass is pulled down by a displacement x and eleased it will undego SHM. The net upwads foce will be: This can be multiplied out to become: Since ke mg this can become: T ke mg F ( k( e x) mg) F ( ke kx mg) F ( mg kx mg) It simplify to: F kx Since both F ma and a ( f ) x (fo SHM) the equation now becomes: This simplifies to: Reaanging fo f gives us: And since kx m( f ) k ( f ) m f m f the equation becomes: T T k Time is measued in seconds, s Finding g We can find the value of the gavitational field stength, g, on Eath by caying out the following expeiment. Set up a simple pendulum of length l and measue the time fo one oscillation. If we measue the time taken fo oscillations and divide it by we educe the pecentage human eo of the eading and make ou expeiment moe accuate. l 4 If we look at the equation T and eaange it to become: T l, by plotting a gaph of T g g 4 against l we can find the value of g fom the gadient which will be =. g k m x

9 Lesson 8 Leaning Resonance and Damping To know what fee and foced vibation ae and the phase diffeence between the dive and diven To know what esonance is and how it is eached To know what light, heavy and citical damping ae and thei affects on esonance Fee Vibation Fee vibation is whee a system is given an initial displacement and then allowed to vibate/oscillate feely. The system will oscillate at a set fequency called the natual fequency, f. We have seen fom the last lesson that the time peiod fo a pendulum only depends on the length and gavitational field stength whilst the time peiod of a mass and sping only depends on the mass and the sping constant. These factos goven the natual fequency of a system. Foced Vibation Foced vibation is whee a diving foce is continuously applied to make the system vibate/oscillate. The thing that povides the diving foce will be moving at a cetain fequency. We call this the diving fequency. Resonance If I hold one end of a slinky and let the othe oscillate feely we have a fee vibation system. If I move my hand up and down I foce the slinky to vibate. The fequency of my hand is the diving fequency. When the diving fequency is lowe than the natual fequency the oscillations have a low amplitude When the diving fequency is the same as the natual fequency the amplitude inceases massively, maybe even exponentially. When the diving fequency is highe than the natual fequency the amplitude of the oscillations deceases again. Phase Diffeence between dive and diven When the diving foce begins to oscillate the diven object the phase diffeence is. When esonance is achieved the phase diffeence between them is π. When the diving fequency inceases beyond the natual fequency the phase diffeence inceases to π/. Damping Damping foces oppose the motion of the oscillating body, they slow o stop simple hamonic motion fom occuing. Damping foces act in the opposite diection to the velocity. Galileo made an impotant obsevation while watching lamps swing in Pisa cathedal. He noticed that the swinging gadually died away but the time taken fo each swing stayed oughly the same. The swing of the lamp was being damped by ai esistance. Light damping slowly educes the amplitude of the oscillations, but keeps the time peiod almost constant. Heavy damping allows the body to oscillate but bings it quickly to est. Citical damping bings the body back to the equilibium point vey quickly with out oscillation. Ove damping also pevent oscillation but makes the body take a longe time to each equilibium. Damping and Resonance Damping educes the size of the oscillations at esonance. Thee is still a maximum amplitude eached but it is much lowe than when the system is undamped. We say that damping educes the shapness of esonance. This becomes cleae if we look at the gaph on the ight. It shows the amplitude of oscillation against fequency fo diffeent levels of damping.

10 Lesson 9 Leaning Gavitational Fields To be able to calculate the foce of gavity between two masses To be able to explain what gavitational field stength is To be able to calculate the gavitational field stength at a distance fom the cente Newton s Law of Gavitation (Gavity) (Also seen in GCSE Physics ) Gavity is an attactive foce that acts between all masses. It is the masses themselves that cause the foce to exist. The foce that acts between two masses, m and m, whose centes ae sepaated by a distance of is given by: mm F This was tested expeimentally in a lab using lage lead sphees and was efined to become: Gmm F G is the Gavitational Constant, G = 6.67 x - N m kg - When one of the masses is of planetay size, M, the foce between it and a test mass, m, whose centes ae sepaated by a distance of is given by: m F The minus sign means that the foce is attactive, the foce is in the opposite diection to the distance fom the mass (displacement). This will become cleae when we look at the electic foce. Negative = Attactive Positive = Repulsive Foce is measued in Newtons, N Gavitational Fields A gavitational field is the aea aound a mass whee any othe mass will expeience a foce. We can model a field with field lines o lines of foce. Radial Fields The field lines end at the cente of a mass and tail back to infinity. We can see that they become moe spead out the futhe fom the mass we go. Unifom Fields The field lines ae paallel in a unifom field. At the suface of the Eath we can assume the field lines ae paallel, even thou they ae not. Gavitational Field Stength, g We can think of gavitational field stength as the concentation of the field lines at that point. We can see fom the diagams above that the field stength is constant in a unifom field but dops quickly as we move futhe out in a adial field. The gavitational field stength at a point is a vecto quantity and is defined as: The foce pe unit mass acting on a small mass placed at that point in the field. F We can epesent this with the equation: g m If we use ou equation fo the gavitational foce at a distance and substitute this in fo F we get: m g which simplifies to: g m Gavitational Field Stength is measued in Newtons pe kilogam, N kg -

11 Lesson Leaning Gavitational Potential To be able to explain what gavitational potential is and be able to calculate it To know how gavitational potential is linked to potential enegy and be able to calculate it To be able to sketch gaphs of potential and field stength ove distance fom suface Gavitational Potential, V The gavitational potential at a point fom a planet o mass is defined as: The wok done pe unit mass against the field to move a point mass fom infinity to that point The gavitational potential at a distance fom a mass M is given by: V The value is negative because the potential at infinity is zeo and as we move to the mass we lose potential o enegy. Gavitational potential is a scala quantity. The gavitational field is attactive so wok is done by the field in moving the mass, meaning enegy is given out. Gavitational Potential is measued in Joules pe kilogam, J kg - Gavitational Potential Enegy (Also seen in AS Unit ) In Unit we calculated the gavitational potential enegy of an object of mass m at a height of h with: E P mgh This is only tue when the gavitational field stength does not change (o is constant) such as in a unifom field. Fo adial fields the gavitational field stength is given by g We can use this to help us calculate the gavitational potential enegy in a adial field at a height. E P mgh E P m E P m (We have dopped the negative sign because enegy is a scala quantity) If we look at the top equation fo gavitational potential we can see that the gavitational potential enegy can be calculated using: E P mv The wok done to move an object fom potential V to potential V is given by: W m( V V) which can be witten as W mv Gavitational Potential Enegy is measued in Joules, J Gaphs Hee ae the gaphs of how gavitational field stength and gavitational potential vay with distance fom the cente of a mass (eg planet). In both cases R is the adius of the mass (planet). The gadient of the gavitational potential gaph gives us the gavitational field stength at that point. To find the gadient at a point on a cuve we must daw a tangent to the line then calculate the gadient of the tangent: y V gadient g x If we eaange the equation we can see whee we get the top equation fo gavitational potential. V g g V sub in the equation fo g V V V

12 Lesson Leaning Obits and Escape Velocity To be able to calculate the obital speed of a satellite if given the height fom the Eath To be able to calculate the time of obit of a satellite if given the height fom the Eath To be able to calculate the escape velocity fom a planet Obits (Also seen in GCSE Physics ) Fo anything to stay in obit it equies two things: *A centipetal foce, caused by the gavitational foce acting between the object obiting and the object being obited *To be moving at a high speed We now know equations fo calculating the centipetal foce of an object moving in a cicle of adius AND fo calculating the gavitational foce between two masses sepaated by a distance of. Centipetal foce at distance : F mv o F m o mv F m Gavitational foce at distance : F These foces ae equal to each othe, since it is the foce of gavity causing the centipetal foce. Fom these we can calculate many things about an obiting object: The speed needed fo a given adius mv m v v The time of obit fo a given adius m m 4 T ( f ) T T 4 4 T Enegy of Obit The total enegy of a body in obit is given by the equation: E T mv v T Total enegy = Kinetic enegy + Potential enegy o ET EK EP m E T m m E T m m 4 E T m Geostationay Obits (Also seen in GCSE Physics ) Geostationay obiting satellites obit aound the equato fom West to East. They stay above the same point on the equato meaning that the time peiod is 4 hous o seconds. They ae used fo communication satellites such as television o mobile phone signals. Escape Velocity Fo an object to be thown fom the suface of a planet and escape the gavitational field (to infinity) the initial kinetic enegy it has at the suface must be equal to the potential enegy (wok done) to take it fom the suface to infinity. Potential enegy: E P m R Kinetic enegy: mv m R Fo an object to be escape the Eath.. v R v R v R EK mv v 4 (6.67 )(6. ) v v = 8 m/s 6 (6.4 ) R This calculation is unealistic. It assumes that all the kinetic enegy must be povided instantaneously. We have multistage ockets that povide a continuous thust.

13 Lesson Leaning Electic Fields To be able to calculate the foce of gavity between two chages To be able to explain what electic field stength is To be able to calculate the electic field stength at a distance fom the cente Coulomb s Law (Electic Foce) (Also seen in GCSE Physics ) The electostatic foce acts between all chaged paticles and can be attactive o epulsive. It is the chages themselves that cause the foce to exist. The foce that acts between two chages, Q and Q, whose centes ae sepaated by a distance of is given by: Q Q F Like chages Opposite chages Like chages The popotional constant was found and the equation becomes: QQ F 4 ε is the Pemittivity of Fee Space, ε = x - F m - When one of the chages is lage, Q, the foce between it and a test chage, q, whose centes ae sepaated by a distance of is given by: Qq F 4 If the two chages ae positive, (+Q)(+q) = + Qq A positive foce means the chages epel. If the two chages ae negative, ( Q)( q) = + Qq A positive foce means the chages epel. If one is negative and one is positive, ( Q)(+q) = Qq A negative foce means the chages attact. Electic Fields An electic field is the aea aound a chage whee any othe chage will expeience a foce. We can model a field with field lines o lines of foce. Radial Fields Fo a positive chage the field lines stat at the chage and go out to infinity. Fo a negative chage the field lines end at the cente of a mass and tail back fom infinity. We can see that they become moe spead out the futhe fom the chage we go. Unifom Fields The field lines ae paallel in a unifom field. Between two conducting plates the field lines leave the positive plate and ente the negative plate. Electic Field Stength, E We can think of electic field stength as the concentation of the field lines at that point. We can see fom the diagams above that the field stength is constant in a unifom field but dops quickly as we move futhe out in a adial field. The electic field stength at a point is a vecto quantity and is defined as: The foce pe unit chage acting on a small chage placed at that point in the field F We can epesent this with the equation: E q If we use ou equation fo the electic foce at a distance and substitute this in fo F we get: Qq E 4 q which simplifies to: Q E (RADIAL FIELDS) 4 Electic Field Stength is measued in Newtons pe Coulomb, N C -

14 Lesson Leaning Electic Potential To be able to explain what electic potential is and be able to calculate it To know what the field stength is like in a unifom field and how it is linked to electic potential To be able to sketch gaphs of potential and field stength ove distance fom suface Electic Potential, V The electic potential at a point fom a point chage is defined as: The wok done pe unit chage against the field to move a positive point chage fom infinity to that point The electic potential at a distance fom a chage Q is given by: Q V 4 The value will be positive when wok is done against the field (when like chages ae epelling). The value will be negative when wok is done by the field (when opposite chages attact). In both cases the potential at infinity is zeo. Electic potential is a scala quantity. Electic Potential is measued in Joules pe Coulomb, J C - Electic Potential Diffeence (Also seen in GCSE Physics and AS Unit ) Electic potential is the wok done pe unit chage which can be witten like this: W V Q We came acoss this equation in the QVIRt lesson of Unit. We used it to define the potential diffeence as the enegy given to each chage. Fom what we have just defined we can now update ou definition of potential diffeence. Potential diffeence is the diffeence in electic potential between two points in an electic field. The wok done to move a chage fom potential V to potential V is given by: W Q( V V) which can be witten as W QV Unifom Fields In a unifom field like that between two conducting plates the field stength is constant as we have aleady seen. Now that we undestand electic potential we can use an equation fo the field stength in a unifom field. V E Whee V is the potential diffeence between the plates and d is the sepaation of the plates. d Electic Field Stength can be measued in Volts pe mete, V m - Gaphs Hee ae the gaphs of how electic field stength and electic potential vay with distance fom the cente of a chaged sphee. In both cases R is the adius of the sphee. The gadient of the electic potential gaph gives us the electic field stength at that point. To find the gadient at a point on a cuve we must daw a tangent to the line then calculate the gadient of the tangent: y V gadient E x If we eaange the equation we can see whee we get the top equation fo electic potential. V Q Q E E V sub in the equation fo E V V 4 4 Q 4 V

15 Lesson 4 Leaning Fields Compaison To be able to descibe and explain the motion of a chaged paticle in an electic field To be able to state the similaities between gavitational and electic fields To be able to state the diffeences between gavitational and electic fields Motion in an Electic Field A chaged paticle moving though an electic field will feel a foce towads the oppositely chaged plate. We see that the electon moves in a paabola towads the positive plate and the positon moves towads the negative plate. The field stength is constant so the foce is the same at all points in the field and is given by F qe. The diection of the foce depends on the chage of the paticle enteing the field Like the pojectiles we looked at duing AS Unit, the vetical velocity is independent fom the hoizontal velocity. The acceleation in the vetical plane will be equal to E and it will feefall like a mass in a gavitational field. Compaing Fields We have seen that the chaacteistics of gavitational and electic fields have some similaities and diffeences. Gavitational Fields Electic Fields Foce is between Masses Chages Constant of G popotionality 4 Equation fo foce Natue of foce Definition of field stength Field stength in adial field Definition of potential Potential Potential at infinity Wok done moving between points of diffeent potential Gadient of potential against distance gaph Gmm F Newton (N) Vecto Attactive only Foce pe unit mass g Newtons pe kilogam (N/kg) Vecto The wok done in binging a unit mass fom infinity to the point in the field V Joules pe kilogam (J/kg) Scala QQ F 4 Newtons (N) Vecto Like chages epel Diffeent chages attact Foce pe unit chage Q E 4 Newtons pe Coulomb (N/C) Vecto The wok done in binging a unit chage fom infinity to the point in the field Q V 4 Joules pe Coulomb (J/C) Scala W mv Joules (J) Scala Field stength W QV Joules (J) Scala Field stength

16 Lesson 5 Leaning Capacitos To be able to calculate capacitance To be able to explain what happens as a capacito chages up To be able to deive the enegy stoed by a capacito Capacitos A capacito is an electonic component that can stoe electical chage and then elease it. It is made of two conducting plates sepaated by an insulato. The chage that is stoed by the capacito is due to the potential diffeence acoss. We can wite this as: Q V o Q = kv k is a constant specific to the capacito, this is called the capacitance and is epesented by the symbol C Q CV Capacitance is measued in Faads, F Chage is measued in Coulombs, C We can eaange the equation into C = Q / V and fom this we can see that capacitance is a measue of the chage stoed pe volt of potential diffeence. Faad means Coulomb of chage is stoed pe Volt. Wate Analogy We can think of the chage stoed by a capacito as the volume of wate in a bucket. The coss-sectional aea of the bucket epesents the capacitance of the capacito. We can see that the capacitance of capacito is highe than the capacitance of capacito. The height of the wate epesents the potential diffeence acoss the capacito. We can see that the potential diffeence acoss capacito is highe than the p.d. acoss capacito. The chage stoed by both capacitos is the same. A capacito with a lowe capacitance can stoe moe chage if the p.d. acoss it is inceased. Chaging and Dischaging When a capacito is connected to a battey is sends out electons to one of the plates, this becomes negatively chaged. The same amount of electons move fom the second plate and ente the battey, leaving the plate positively chaged. The capacito is now stoing a chage o is chaged. If the chaged capacito is disconnected fom the battey and connected to a lamp it will give out the stoed chage o will dischage. The electons on the negative plate move though the cicuit and onto the positive plate. The plates now have no chage on them. The enegy stoed by the capacito is tansfeed to the bulb whilst the electons move (whilst a cuent flows). Enegy Stoed by a Capacito The top equation shows us that the chage of a capacito inceases with the potential diffeence acoss it. If we plotted p.d. against chage we get a gaph that looks like this We can deive an equation to find the enegy that a capacito stoes by consideing the enegy tansfeed duing the shaded section on the lowe gaph. In this section the chage changes fom q to q+δq when an aveage p.d. of v is applied acoss it. Using E = VQ (see AS Unit ) the enegy stoed is E = v Δq. The total enegy is equal to the total of all the little ectangula sections and is given by E = ½ QV. This is also equal to the aea unde the gaph. We can use the top equation to deive two moe equations fo the enegy stoed by a capacito: E QV CV Q E E C Enegy is measued in Joules, J

17 Lesson 6 Leaning Chaging and Dischaging To be able to sketch gaphs of chage, p.d. and cuent ove time fo a chaging capacito To be able to sketch gaphs of chage, p.d. and cuent ove time fo a dischaging capacito To be able to calculate the time constant and state its significance In the diagam to the ight a capacito can be chaged by the battey if the switch is moved to position A. It can then be dischaged though a esisto by moving the switch to position B. Chaging a Capacito When the switch is moved to A the battey sends electons to the lowe plate and takes them fom the uppe plate. This leaves the lowe plate negatively chaged and the uppe plate positively chaged. An electic field is set up between the plates. Cuent The cuent is the flow of electons though the cicuit (see Unit ). Thee is a lage cuent initially as electons move to the lowe plate. As time passes and moe electons ae on the plate it becomes moe difficult to add moe due to the electostatic epulsion of simila chages. When no moe electons move in the cicuit the cuent dops to zeo. Chage The chage stoed by the capacito inceases with evey electon the moves to the negative plate. The amount of chage inceases quickly at the beginning because a lage cuent is flowing. As the cuent dops the ate at which the chage inceases also dops. A maximum chage is eached. P.D. Since potential diffeence is popotional to chage, as chage builds up so does p.d. The maximum value of p.d. is eached as is equal to the teminal p.d. of the battey. Dischaging a Capacito When the switch in moved to B the electons on the negative plate epel each othe and move back into the cicuit. Eventually both plates lose thei chage and the electic field between them disappeas. Cuent Thee is initially a lage cuent as the electons leave the negative plate. As the numbe of electons on the negative plate falls so does the size of the epulsive electostatic foce, this makes the cuent fall at a slowe ate. When no moe electons move in the cicuit the cuent dops to zeo. Chage The chage that was stoed on the plates now falls with evey electon that leaves the negative plate. The chage falls quickly initially and then slows, eventually eaching zeo when all the chage has left the plates. P.D. As the chage falls to zeo so does the potential diffeence acoss the capacito. Time Constant, τ The time it takes fo the capacito to dischage depends on the time constant. The time constant is the time it takes fo the chage o p.d. of a capacito to fall to 7% of the initial value. OR The time constant is the time it takes fo the chage o p.d. of a capacito to fall by 6% of the initial value. It is given by the equation: RC If the capacito has a lage capacitance it means it can hold moe chage, this means it will take longe to dischage. If the esisto has a lage esistance it means it is hade to move the electons aound the cicuit, this also means it will take longe to dischage.

18 Lesson 7 Leaning Exponential Decay To be able to calculate the chage of a dischaging capacito afte a time, t To be able to calculate the potential diffeence acoss a dischaging capacito afte a time, t To be able to calculate the cuent though a dischaging capacito afte a time, t Finding τ fom Gaphs The time constant of a dischaging capacito can be found fom a gaph of eithe chage, cuent o potential diffeence against time. Afte one time constant the value will have dopped to.7 of the initial value. In this case the time constant is 4 seconds. Quantitative Teatment We could use the gaph above to find the chage on the capacito afte a time, t. We could also use it to find the time it takes fo the chage to fall to a value of Q. This equies the gaph to be dawn vey accuately and values need to be taken fom it vey caefully. Instead of doing this we can use the following equation to calculate the chage, Q afte a time, t. t / RC Q Q e t is the time that has elapsed since dischage began Q is the emaining chage Q is the initial (o stating) chage RC is the time constant, also equal to the esistance multiplied by the capacitance. Time is measued in seconds, s When the time elapsed is equal to the time constant the chage should have fallen to 7% of the initial value. t / RC RC / RC Q Q e Q Q e Q Q e (but e - =.7) Q Q. 7 When the time elapsed is equal to twice the time constant the chage should have fallen to 7% of 7% of the initial value. t / RC RC / RC Q Q e Q Q e Q Q e (but e - =.7 x.7) Q Q. 4 Simila equations can be established fo the cuent flowing though and the potential diffeence acoss the capacito afte time, t: Q Q e t / RC I I e t / RC V V e Reaanging The equations above can be eaanged to make t the subject. We will use the equation fo chage: t / RC t RC Q Qe Q Q e / t Q Q ln Q RC Q ln RC t Q ln RC t Q They can also be eaanged to make RC (time constant) the subject: t / RC t RC Q Qe Q Q e / ln t Q RC Q RC t Q ln Q t / RC

19 Lesson 8 Leaning Foce on a Cuent Caying Wie To be able to explain why a wie with a cuent flowing though it will expeience a foce To be able to calculate the size of the foce on the wie To be able to state the diection of the foce on the wie We will be looking at the foce a cuent caying wie expeiences when it is in a magnetic field. Befoe we look into the size and diection of the foce we need to establish some basics. Conventional Cuent We know that the cuent flowing in a cicuit is due to the negative electons flowing fom the negative teminal of a battey to the positive teminal. Negative to Positive is the flow of electons Befoe the discovey of the electon scientist thought that the cuent flowed fom the positive teminal to the negative one. By the time the electon was discoveed many laws had been established to explain the wold aound them using cuent as flowing fom positive to negative. Positive to Negative is the Conventional Cuent Magnetic Field Lines We ae familia with the shape of a magnetic field aound a ba magnet. Magnetic field lines leave the Noth Pole of the magnet and ente the South Pole. The poles of a magnet ae stonge than the side because thee ae moe field lines in the same aea of space. Magnetic field lines go fom Noth to South A D Poblem We will be looking at movement, fields and cuents in D but ou page is only D. To solve this poblem we will use the following notation: A dot means coming out of the page and a coss means going into the page. Imagine an aow fied fom a bow, pointy end means it s coming towads you, coss means its moving away. out of the page, into the page Cuent Caying Wies When a cuent flows though a staight piece of wie it ceates a cicula magnetic field. The Right Hand Gip Rule shows us the diection of the magnetic field. If we use ou ight hand and do a thumbs up the thumb is the diection of the conventional cuent and the finges point the diection of the field lines. Right hand thumbs up Foce on a Cuent Caying Wie When a wie is placed between a Noth and South Pole (in a magnetic field), nothing happens. When a (conventional) cuent flows though the wie it expeiences a foce due to the magnetic fields of the magnet and the wie. If we look at the diagam we can see that the magnetic field lines above ae moe compact than below. This foces the wie downwads. Fleming s Left Hand Rule This ule links the diections of the foce, magnetic field and conventional cuent which ae all at ight angles to each othe. You fist finge points fom Noth to South, you middle finge points fom positive to negative and you thumb points in the diection of the foce. Size of the Foce The size of the foce on a wie of length l, caying a cuent I placed in a magnetic field of magnetic flux density B is given by the equation: F BIl Hee the wie is at 9 to the magnetic field lines. When the wie is at an angle of θ with the magnetic field the foce is given by: F BIl sin F If we eaange the equation to B we see that Tesla is the magnetic flux density (field stength) that Il causes a Newton foce to act on mete of wie caying Amp of cuent. Magnetic Flux Density is measued in Tesla, T This equation looks vey familia if we compae it to the foce in a gavitational and electic field. F m. g F q. E F Il. B

20 Lesson 9 Leaning Foce on a Chaged Paticle To be able to calculate the size and diection of the foce on a chaged paticle in a magnetic field To be able to descibe the motion of a chaged paticle in a magnetic field To be able to descibe the main featues of a cycloton and explain how it woks Foce on Chaged Paticle Fom ou equation fo the foce a magnetic field will exet on a wie we can deive a equation fo the foce it will exet on a single chaged paticle. Stat with F BIl. In Unit we defined the cuent as We can ewite this equation l F BQ and use t Q Q I so we can sub this in to become F B l t t l v fom Unit to aive at the equation: F BQv t Moving in a Cicle If a chaged paticle entes a magnetic field it will feel a foce. We now know the size of the foce (given by equation above) and diection of the foce (given by Fleming s Left Hand Rule). If we use the left hand ule in the diagam to the ight we can see that the foce is always at ight angles to the velocity. Fist finge points into the page, middle finge points along the line and ou thumb points upwads. While the paticle is in the magnetic field it will move in a cicle. Radius of the cicle We can calculate the adius a chaged paticle will move in by using ou equation fo the foce on a chaged paticle in a magnetic field and a centipetal foce equation. mv mv F BQv and F ae equal to each othe so we can wite BQv Time fo a complete cicle We can also calculate the time it takes fo the chaged paticle to move in one complete cicle. mv BQv mv Stating at F mv we can use f to make the equation become F mvf and then F T The centipetal foce is due to the magnetic foce on the chaged paticle so we can put these equal to each mv m m othe. BQv cancel the v to become BQ which eaanges to: T T T BQ So the time it takes to complete a full cicle does not depend on the velocity. The Cycloton A cycloton is a paticle acceleato. It consists of two hollow D-shaped electodes (called dees ) that ae attached to an altenating p.d. supply. The dees ae placed in vacuum chambe and a magnetic field which acts at ight angles to them. A paticle will move in a cicle because of the magnetic field. When it eaches the gap between the dees the altenating supply has made the othe dee have the opposite chage to the paticle. This causes the paticle to acceleate acoss the gap and ente the second dee. This continues to happen until the paticle is moving at the equied speed. At this point it leaves the cycloton. The Mass Spectomete A mass spectomete is used to analyse the types of atom that ae in a sample. The atoms ae given a chage, acceleated and sent into a magnetic field. If we look at the adius equation above we can see that atoms tavelling at the same speed in the same magnetic field given the same chage will be deflected based on thei mass. Heavy atoms will move in bigge cicles than lighte ones. Pai Poduction If we think back to Unit we saw this phenomenon in action. Pai poduction is when a photon of enegy is conveted into a paticle and an antipaticle, such as an electon and a positon. If this happens in a magnetic field the electon will move in a cicle in one diection and the positon will move in a cicle in the othe diection. mv BQ

21 Lesson Leaning Magnetic Flux and Flux Linkage To be able to calculate and explain the magnetic flux though a coil of wie To be able to calculate the magnetic flux linkage of a coil of wie To be able to calculate the magnetic flux linkage of a otating coil Magnetic Flux, Magnetic flux is a measue of how many magnetic field lines ae passing though an aea of A m. The magnetic flux though an aea A in a magnetic field of flux density B is given by: BA This is when B is pependicula to A, so the nomal to the aea is in the same diection as the field lines. Magnetic Flux is measued in Webes, Wb The moe field pass though aea A, the geate the concentation and the stonge magnetic field. This is why a magnet is stongest at its poles; thee is a high concentation of field lines. We can see that the amount of flux flowing though a loop of wie depends on the angle it makes with the field lines. The amount of flux passing though the loop is given by: θ is the angle that the nomal to the loop makes with the field lines. Magnetic Flux Density We can now see why B is called the magnetic flux density. If we eaange the top equation fo B we get: B So B is a measue of how many flux lines (field lines) passes though each unit aea (pe m ). A A flux density of Tesla is when an aea of mete squaed has a flux of Webe. Flux Linkage We now know that the amount of flux though one loop of wie is: BA If we have a coil of wie made up of N loops of wie the total flux is given by: N BAN The total amount of flux, N, is called the Magnetic Flux Linkage; this is because we conside each loop of wie to be linked with a cetain amount of magnetic flux. Sometimes flux linkage is epesented by, so N which makes ou equation fo flux linkage BAN Flux Linkage is measued in Webes, Wb Rotating Coil in a Magnetic Field If we have a ectangle of wie that has an aea of A and we place it in a magnetic field of flux density B, we have seen that the amount of flux flowing though the wie depends on the angle between it and the flux lines. The flux linkage at an angle θ fom the pependicula to the magnetic field is given by: N BAN cos Fom ou lessons on cicula motion we established that the angula speed is given by which can be t eaanged to t and substituted into the equation above to tansfom it into: N BAN cos t When t = the wie is pependicula to the field so thee is a maximum amount of flux. At the flux linkage is a maximum in one diection. Thee is the lowest ate of change at this point. At the flux linkage is zeo. Thee is the biggest ate of change at this point At the flux linkage is maximum but in the opposite diection. The lowest ate of change occus hee too. At 4 the flux linkage is zeo. Thee is the biggest ate of change at the point too but in the opposite diection. Next lesson we will be looking at inducing an e.m.f. using a wie and a magnetic field. The size of the e.m.f. depends on the ate of change of flux linkage.

22 Lesson Leaning Electomagnetic Induction To know how emf and cuent ae induced To know Faaday s Law and be able to use it to descibe the induced emf To know Lenz s Law and be able to use it to descibe the induced emf Making Electicity (Also seen at GCSE Physics ) An e.m.f. can be induced acoss the ends of a conducting wie in two ways: ) Move the wie though a magnetic field o ) Move a magnet though a coil of the wie In both cases magnetic field lines and wies ae cutting though each othe. We say that the wie is cutting though the magnetic field lines (although it is fai to say that the field lines ae cutting though the wie). If the conducto is pat of a complete cicuit a cuent will be induced though it as well as an e.m.f. acoss it. Thee ae two laws that descibe the induced e.m.f... Faaday s Law Size of induced e.m.f. The magnitude of the e.m.f. induced in a conducto equals the ate of change of flux linkages o the ate at which the conducto cuts a magnetic flux. Staight Wie Imagine a staight piece of wie of length l is moved though a magnetic field at a velocity v. If the wie is moving at ight angles to the field lines an e.m.f. is induced (because field lines ae being cut). The size of the e.m.f. is given by the equation: N t Fo one loop of wie BA and the flux is given by BA which ae combine to become t t BA B is constant so. ΔA is the aea the wie cuts though in a time t and is given by A l. vt so we get: t Bl. vt Blvt The length of the wie and velocity ae constant so it becomes which cancels to: Blv t t Rotating Coil of Wie If we have a coil of wie with N tuns, each of which has an aea of A and placed it a magnetic field of flux density B nothing would happen. If it was otated with an angula speed of ω it would cut though the magnetic field lines and an e.m.f. would be induced. The size of the e.m.f. is given by: ( BAcos t) Since N and BAcos t we get N and if we diffeentiate it: BAN sint t t This is why the Mains supply is altenating; the otating coil cuts the field lines in one diection on the way up and the othe diection on the way down. Lenz s Law Diection of induced e.m.f. The diection of the e.m.f. induced in a conducto is such that it opposes the change poducing it. Solenoid (Right Hand Gip Rule) A solenoid with a cuent flowing though it poduces a magnetic field like that of a ba magnet. We can wok out which end is the Noth Pole and which is the South by using the Right Hand Gip Rule fom ou foce on a wie lesson. If ou finges follow the diection of the cuent though the coils ou thumb points out of the Noth Pole. *When we push the Noth Pole of a magnet the induced cuent in the solenoid flows to make a Noth Pole to epel the magnet. *When we pull the Noth Pole out of the solenoid the induced cuent flows to make a South Pole to attact the magnet. Fleming s Right Hand Rule If we ae just moving a staight wie though a unifom magnetic field the diection of the induced cuent can be woked out using Fleming s Right Hand Rule. You fist finge points in the diection of the field fom Noth to South, you thumb points in the diection the wie is moved and you middle finge points in the diection of the conventional cuent.

23 Lesson Leaning Tansfomes To be able to descibe a tansfome and calculate the voltage and cuent in the seconday coil To be able to calculate the efficiency of a tansfome and explain why they ae used To be able to state the causes of inefficiency in tansfomes Tansfomes (Also seen at GCSE Physics ) A tansfome is a device used to change the voltage/cuent of a cicuit using electomagnetic induction. It consists of a soft ion coe wapped on both side with wie. The fist coil of wie is called the pimay coil and the othe coil of wie is called the seconday coil. A cuent doesn t flow fom one coil of wie to the othe. How They Wok A cuent flows though the pimay coil which ceates a magnetic field. As this field is established the field lines cut though the tuns of wie on the seconday coil. This induces an e.m.f. (voltage) and a cuent in the second coil. Since the supply to the pimay coil is constantly changing diection the magnetic field is constantly changing diection. This means the seconday coil also has an altenating e.m.f. and cuent. An ion coe is used because it is easily magnetised and demagnetised and conducts the magnetic field. Tansfoming Voltage and Cuent (Also seen at GCSE Physics ) Thee ae two types of tansfomes: Step Up The voltage in the seconday coil is lage than the voltage in the pimay coil. The cuent in the seconday coil is smalle than the cuent in the pimay coil. Thee will be moe tuns of wie on the seconday coil meaning moe flux linkage Step Down The voltage in the seconday coil is smalle than the voltage in the pimay coil. The cuent in the seconday coil is lage that the cuent in the pimay coil. Thee will be fewe tuns of wie on the seconday coil meaning less flux linkage In both cases the voltage and cuent (V P and I P ) in the pimay coil of N P tuns is linked to the voltage and cuent (V S and I S ) in the seconday coil of N S tuns by the following equation: N S VS I P N V I P The National Gid (Also seen at GCSE Physics ) The National Gid is a system of tansfomes that inceases the voltage (educing the cuent) of an altenating electical supply as it leaves the powe station. Thick cables held above the gound by pylons cay the supply to ou neighbouhood. A second seies of tansfomes lowes the voltage to a safe level and inceases the cuent to be used in ou homes. Why Bothe? Enegy is lost in the tansmission of electicity. The electons flowing in the wie ae constantly colliding with the positive ions of the metal that the wie is made fom. If we incease the voltage of a supply this lowes the cuent. Loweing the cuent educes the numbe of collisions happening pe second hence educing the amount of enegy lost in eaching ou homes. The cables that cay the cuent have a lage coss sectional aea, this lowes the esistance and enegy lost. Efficiency of a Tansfome The efficiency of a tansfome can be calculated using the following equation: P I SV Efficiency I V The efficiency of a tansfome can be inceased by: *Using low esistance windings to educe the powe wasted due to the heating effect of the cuent. *Use a laminated coe which consists of layes of ion sepaated by layes of insulation. This educes heating in the ion coe and cuents being induced in the coe itself (efeed to as eddy cuents). P S S P

24 Unit 5 Lesson Leaning Ruthefod Scatteing To know the set up of Ruthefod s expeiment and the esults he found To be able to explain how the esults ae evidence fo the nucleus To know the factos we must conside when choosing the paticle we will scatte Ruthefod s Scatteing Expeiment (Also seen in GCSE Physics ) Hans Geige and Enest Masden woked with Enest Ruthefod in his Mancheste laboatoies in 99. They fied alpha paticles (which they knew to have a positive chage) of a few MeV into a thin piece of gold foil. This was done in an evacuated chambe connected to a vacuum pump. When the alpha paticles passed though the gold foil they hit a zinc sulphide sceen which emits light wheneve an alpha paticle stikes it. This sceen was obseved using a moving micoscope in a dak oom. At the time the accepted stuctue of the atom was like a plum pudding: positive dough spead evenly with negative electons scatteed though out it like plums in a pudding. Results (Also seen in GCSE Physics ) Geige and Masden found that almost all of the alpha paticles passed though with little o no deflection. Ruthefod suggested moving the micoscope in font of the foil, when they did they found that about in evey 8 was eflected back o scatteed though an angle of moe that 9. If the plum pudding model was the stuctue of the atom this would be like fiing a bullet at a piece of toilet pape and it bouncing back mental! The Nuclea Model (Also seen in GCSE Physics ) Ruthefod used these esults to make the following conclusions: Most of the mass must be gatheed in one small volume the nucleus. They can epel a fast moving alpha paticle The nucleus must be positively chaged. They epel positive alpha paticles Most of the atom is empty space. Only in 8 alpha paticles ae deflected Negative electons obit the nucleus at a lage distance fom it. Negative chages ae needed to keep the atom neutal Which Paticle to Use? Thee ae two things to conside when using scatteing to find the stuctue of things: the paticle and the enegy Alpha Scatteing: Ruthefod used alpha paticles with enegies aound 4MeV, any highe and it would be close enough to the nucleus to expeience the stong nuclea foce. Electon Scatteing: Electons ae acceleated to high enegies of aound 6GeV. They have enough enegy to be scatteed within potons and neutons; discoveing quaks. Electons tavelling at this speed have a de Boglie wavelength times smalle than visible light meaning we can see moe detail. X-ay Scatteing: X-ay photons have shot wavelengths and can be scatteed o completely absobed by atomic electons. If the electon is tightly bound o the photon has vey little enegy the electon emains in the atom and the photon loses no enegy. This is known as elastic o coheent scatteing. If the photon has enough enegy it knocks the electon out of obit (ionisation) and does lose enegy. Neuton Scatteing: Vey useful because they ae not chaged but this limits the enegies they can be acceleated to. Neutons inteact weakly with othe nuclei and do not inteact with electons at all, because of this they can penetate futhe. Thei wavelengths ae simila to that of atomic spacing, meaning that diffaction will occu.

25 Unit 5 Lesson Leaning Ionising Radiation To know what alpha, beta and gamma ae and be able to list thei uses and danges To know the invese-squae law of adiation and be able to calculate intensity at given distances To know what backgound adiation is and what contibutes to it Ionisation (Also seen in GCSE Physics ) The pocess of ionisation involves the emoval of one o moe electon fom an atom. When adiation entes a tube it may ionise the atoms inside, the electons ae attacted to a positive wie and a small cuent flows. Thee ae thee types of adiation, each with its own popeties, uses and danges. Alpha: A Helium nucleus two potons and two neutons Relative mass: 4 Relative chage: + Deflection by E/M field: Yes Ionising powe: High Penetating powe: Low Range in ai: 5cm Stopped by: Skin, pape Uses: Smoke detectos, adiotheapy to teat cance Dange out of body: Low Dange in body: Cell death, mutation and cance Beta: A fast moving electon Relative mass: / Relative chage: - Deflection by E/M field: Yes Ionising powe: Medium Penetating powe: Medium Range in ai: -m Stopped by: Aluminium Uses: Thickness contol in pape poduction Dange out of body: Damage to skin Dange in body: Simila to alpha but less damage Gamma: A high fequency electomagnetic wave Relative mass: Relative chage: Deflection by E/M field: No Ionising powe: Low Penetating powe: High Range in ai: 5m Slowed by: Lead, concete Uses: Taces: medical and industial, steilising sugical equipment Dange out of body: Cell death, mutation and cance Dange in body: Low The Invese-Squae Law Gamma adiation fom a souce will spead out. The adiation fom a small souce can be consideed the same in all diections (isotopic), imagine a sphee aound the souce. As we move futhe away fom the souce the bigge the sphee gets. The same amount of enegy is shaed ove a geate suface aea. The futhe we move fom the souce the less intensity of the gamma adiation. Intensity is measued in Watts, W The intensity, I, of the adiation at a distance x fom the souce is given as Whee I is the intensity at the souce and k is a constant. We do not always need to know the intensity at the souce to find it at a given distance. Conside two points, A and B, a cetain distance away fom a gamma souce. ki ki I A I A( xa) ki and I B I B ( xb ) ki ( x A ) ( x B ) We can combine these to give I A( xa) ki I B ( xb ) ki I x I A( xa) I B ( xb Backgound Radiation (Also seen in GCSE Physics ) We ae continuously exposed to a cetain level of backgound adiation. In the lessons to come you must emembe to subtact the backgound adiation fom the ecoded adiation level to get the tue (o coected) eading. The main contibutos to backgound adiation ae: Radon and Thoon gas: 5% Gound, ocks and buildings: 4% Food and dink: % Medical: % Cosmic ays: % Ai tavel:.4% Nuclea weapons testing:.% Occupational:.% Nuclea powe:.% )

26 Unit 5 Lesson Leaning Radioactive Decay To know what activity is and how to calculate it To know what the decay constant is and how to calculate it To know what half life is and be able to find it by calculation o gaphical methods Decay (Also seen in GCSE Physics ) Something that is adioactive will decay into something that is stable. Radioactive decay happens andomly and spontaneously: thee is no way of pedicting when a adioactive nucleus will decay and extenal factos do not influence it at all (e.g. pessue and tempeatue). What we can do is give a pobability that a nucleus will decay in a given time. Decay Constant, Evey adioactive isotope has its own pobability that a nucleus will decay, called the decay constant. Activity, A The activity of a adioactive souce is the numbe of decays that happen evey second. becqueel is equal to one decay pe second, 5 becqueels is equal to 5 decay pe second, Activity is measued in becqueels, Bq (decays pe second, s - ) Duing a cetain amount of time, Δt, some adioactive atoms (ΔN) decay fom a sample of N atoms. N The change in the numbe of nuclei in a cetain time is N this can be witten as A N t The minus sign is thee because we ae losing nuclei, the numbe we have left is getting smalle. Exponential Decay As time passes the numbe of nuclei that decay evey second will decease. To calculate the numbe of nuclei that we have left afte a time, t, is given by: Whee N is the numbe of nuclei at the stat and N is the cuent numbe of nuclei. This is simila to the exponential decay equation of a dischaging capacito. The equation fo calculating the activity looks simila: A A e Half-Life (Also seen in GCSE Physics ) Each adioactive isotopes has its own half-life. We aleady know that it is: The time it takes fo the numbe of atoms in a sample to dop to half of its oiginal sample o The time it takes fo the activity of a substance to dop to half of its oiginal activity Half-Life is measued in seconds, s The half life of a substance is linked to the decay constant. If thee is a high pobability that a nucleus will decay ( = BIG) then it will not take long befoe half the sample has decayed to stability (half-life = shot). If thee is a low pobability that a nucleus will decay ( = small) then it will take a long time fo half of the sample to have decayed (half-life = LONG). ln T whee T is the half life N t N e t Gaphs (Also seen in GCSE Physics ) We can calculate the half-life fom activity and numbe of nuclei gaphs. Choose a stating value and then find how long it takes to fall to half this value. In the gaphs we can see that both fall fom 5 to 5 and take 5 hous to do this. Theefoe the half-life is 5 hous. Knowing this we can then calculate the decay constant.

27 Unit 5 Lesson 4 Leaning Modes of Decay To be able to sketch and label a gaph of N against Z fo stable and unstable nuclei To be able to state the changes to the paent nuclei when it undegoes: α decay, β - decay, β + decay, nucleon emission, electon captue and gamma ay emission N Against Z Gaph Hee is a gaph of the numbe of neutons against the numbe of potons in a nucleus. It shows stable and unstable nuclei. Stable nuclei/isotopes ae found on the black line/dots. The shaded aeas above and below the line of stability epesent adioactive isotopes. Why doesn t it follow N=Z? Potons epel each othe with the electomagnetic foce but the stong nuclea foce is stonge at small distances and keeps them togethe in the nucleus. We can see the line of stability follows N=Z at low values. As the nucleus gets bigge thee ae moe potons, when they become a cetain distance apat they no longe expeience the stong nuclea foce that keeps them togethe, only the electomagnetic which pushes them apat. To keep the nucleus togethe we need moe neutons which feel no electomagnetic epulsion only the attaction of the stong nuclea foce. Points to emembe Follows N=Z aound Z=, then cuves to go though Z=8 N= β - emittes above the line, β + emittes below the line and α at the top Alpha Decay (Also seen in GCSE Physics ) An alpha paticle (a Helium nucleus) is ejected fom the paent nucleus. A X 4 4 A Y Z Z Loss: potons, neutons Beta Minus Decay (Also seen in GCSE Physics ) A neuton is tansfomed into a poton (that stays in the nucleus) and an electon (which is emitted). A Z X Beta Plus Decay Y e A Z e Loss: neuton Gain: poton A poton is tansfomed into a neuton and a positon. A A Z X Z Y e e Loss: poton Gain: neuton Electon Captue A nucleus can captue one of the obiting electons. A poton changes into a neuton. A A Z X ez Y e Loss: poton Gain: neuton Nucleon Emission Decay It is possible fo an unstable isotope to emit a nucleon fom the nucleus. In poton-ich o poton-heavy nuclei it is possible (though ae) fo a poton to be emitted. A X A Z Z Y p Loss: poton In neuton-ich o neuton-heavy nuclei it is possible (though ae) fo a neuton to be emitted. X X n Loss: neuton A Z A Z Gamma Ray Emission (Also seen in GCSE Physics ) Alpha emission is often followed by gamma ay emission. The daughte nuclei ae left in an excited state (emembe enegy levels fom Unit ) which they will at some point fall fom to the gound state, emitting a gamma photon. Thee is no nuclea stuctue change, just a change of enegy. A A Z X Z X Loss: Enegy

28 Unit 5 Lesson 5 Leaning Nuclea Radius To be able to calculate the adius of a nucleus by the closest appoach of alpha paticles To be able to calculate the adius of a nucleus by the diffaction angle of electons To be able to calculate the nuclea adius and nuclea density Ruthefod gave us an idea of the size of the nucleus compaed to the atom but moe expeimental wok has been done to find a moe accuate measuement. Closest Appoach of Alpha Paticles Ruthefod fied alpha paticles at gold atoms in a piece of foil. They appoach the nucleus but slow down as the electomagnetic epulsive foce become stonge. Eventually they stop moving, all the kinetic enegy has been conveted into potential enegy as the paticles come to est at a distance fom the cente of the nucleus. E E P qv whee V is the electic potential at a distance of fom the cente K E P Q q 4 E P Q q 4 E K Q q 4 E K This gives us the uppe limit of the adius of a nucleus. Calculating the nuclea adius this way gives us a value of = 4.55 x -4 m o 45.5 fm (whee fm = x -5 m) Moden measuements give us values of appoximately = 6.5 fm (Remembe that ev of enegy is equal to.6 x -9 J) Electon Diffaction A beam of electons wee fied at a thin sample of atoms and the diffaction patten was detected and then examined. The gaph shows a minimum at a value of θ min. We can use this to find a value of the nuclea adius..6 sin min D Whee D is the nuclea adius and λ is the de Boglie wavelength of the beam of electons. We can calculate this as follows: The kinetic enegy gained by the electons is E K ev whee e is the chage on the electon and V is the potential diffeence used to acceleate it. So we now have: mv ev mv ev m v mev m v mev mv mev h We can now substitute this into the equation fo de Boglie wavelength: mv Nuclea Radius Fom the expeimental esults a gaph was plotted of R against A. A gaph like the one to the ight was obtained. They saw that R depends not on A, but on A ⅓. When they plotted the gaph of R against A ⅓ they found a staight line that cut the oigin and had a gadient of. ( is a constant epesenting the adius of a single nucleon and has a value of between. and.5 fm) The adius of a nucleus has been found to be: R A Nuclea Density Now that we have an equation fo the nuclea adius we can calculate the density of a nucleus. h mev If we have a nucleus of A nucleons, we can assume the mass is Au and the volume is the volume of a sphee: m Au Au Au u V 4 R 4 ( A ) 4 A 4 We can see that the density is independent of the nucleon numbe and gives a value of:.4 x 7 kg m -.

29 Unit 5 Lesson 6 Leaning Mass and Enegy To be able to explain what mass defect is and be able to calculate To be able to explain what binding enegy is and be able to calculate To be able to sketch the gaph of B.E. pe nucleon against nucleon numbe Disappeaing Mass The mass of a nucleus is less than the mass of the potons and neutons that it is made of. (mass of potons + mass of neutons) mass of nucleus = m m is the diffeence in the masses and is called the mass defect. Let us look at the nucleus of a Helium atom to see this in action. It is made up of potons and neutons: Mass of nucleons = x (mass of poton) + x (mass of neuton) Mass of nucleons = x (.67 x -7 ) + x (.675 x -7 ) Mass of nucleons = x -7 kg Mass of nucleus = x -7 kg Mass defect = mass of nucleons mass of nucleus Mass defect = x x -7 =.48 x -7 kg As we can see, we ae dealing with tiny masses. Fo this eason we will use the atomic mass unit, u u =.66 x -7 kg The mass defect now becomes =.9 u Paticle Mass (kg) Mass (u) Poton.67 x Neuton.675 x Electon 9. x -.55 Einstein to the Rescue In 95, Einstein published his theoy of special elativity. In this it is stated that: E mc Enegy is equal to the mass multiplied by the speed of light squaed. This means gaining enegy means a gain in mass, losing enegy means losing mass. The evese must be tue. Gaining mass means a gain in enegy, losing mass means a loss in enegy. The enegy we ae losing is the binding enegy. E mc whee m is the mass defect and E is binding enegy Binding Enegy As the potons and neutons come togethe the stong nuclea foce pulls them close and they lose potential enegy. (Like how an object loses its gavitational potential enegy as it falls to the Eath.) Enegy must be done against the s.n.f. to sepaate the nucleus into the nucleons it is made of. This is called the binding enegy (although unbinding enegy would be a bette way to think of it). The binding enegy of the Helium nucleus fom above would be: E = m c E = (.48 x -7 ) x (. x 8 ) E = 4. x - J The Joule is too big a unit to use at the atomic scale. We will use the electon Volt (see AS Unit ) u =.5 x - J and ev =.6 x -9 J u = 9. MeV We can now calculate the binding enegy of the Helium nucleus to be: Binding Enegy Gaph The binding enegy is the enegy equied to sepaate a nucleus into its constituent nucleons. The binding enegy pe nucleon gives us the enegy equied to emove one poton o neuton fom the nucleus. The gaph of binding enegy pe nucleon against nucleon numbe looks like this. Thee is an incease in the enegy equied to emove one nucleon up until the peak of 8.8 MeV at Ion 56. The line then gently deceases. This means Ion is the most stable nucleus because it equies the lagest amount of enegy to emove one nucleon. This will also mean that thee is the geatest mass defect. E = 7 MeV (7 million ev)

30 Unit 5 Lesson 7 Leaning Fission and Fusion To know what occus in nuclea fission and nuclea fusion pocesses To know what a chain eaction is, how it occus and what citical mass is To be able to state and explain whethe fission o fusion will occu Nuclea Fission (Also see GCSE Physics ) Fission occus when a nucleus splits into two smalle nuclei We make fission happen by fiing slow moving neutons at Uanium 5, Plutonium 9 o Thoium nuclei. We call this induced fission. In this pocesses the nucleus absobs a neuton then splits to fom two lighte nuclei, eleases enegy and any neutons left ove, usually o. Hee is a possible equation fo the fission of Uanium 5: U n Ba K n enegyeleased, E Chain Reaction In the above eaction two fee neutons wee eleased, these can also be absobed by two heavy nuclei and cause a fission pocess. These nuclei would elease moe neutons which could cause futhe fissions and so on Citical Mass Fo a chain eaction to happen the mass of the fissionable mateial must be geate than a cetain minimum value. This minimum value is known as the citical mass and is when the suface aea to mass atio is too small. If mass < citical mass: moe neutons ae escaping than ae poduced. If mass = citical mass: numbe of neutons escaping = numbe of neutons poduced. If mass > citical mass: moe neutons ae poduced than ae escaping. Stops Steady Meltdown Nuclea Fusion (Also see GCSE Physics ) Fusion occus when two nuclei join to fom a bigge nucleus The two nuclei must have vey high enegies to be moving fast enough to ovecome the electostatic epulsion of the potons then, when close enough, the stong nuclea foce will pull the two nuclei togethe. Hee is an example of the fusing of two hydogen isotopes: 4 H H He n enegyeleased, E Which Will Happen? Looking at the gaph we can see the Ion 56 has the highest binding enegy pe nucleon, the most enegy equied to emove one poton o neuton fom the nucleus. This makes it the most stable. Nuclei lighte than Ion will undego fusion. Potons and neutons feel the attaction of the stong nuclea foce but only potons feel the epulsion of the electostatic foce. Fo light nuclei, adding an exta poton inceases the stong nuclea foce to pull the nucleon togethe. This is because at this ange the s.n.f. foce is stonge than the othe thee fundamental foces. The nucleons move close togethe potential enegy is lost enegy is given out Nuclei heavie than Ion will undego fission. Beyond Ion, each poton that is added to the nuclei adds to the electostatic epulsion. The bigge the nucleus become the less the oute potons feel the stong nuclea foce fom the othe side. We can see the binding enegy pe nucleon decease fo heavie nuclei. A big nucleus will beak into two smalle nuclei, each being stonge bonded togethe due to the smalle size. The nucleons move close togethe potential enegy is lost enegy is given out.

31 Unit 5 Lesson 8 Leaning Nuclea Reactos To be able to explain how a nuclea eacto poduces electicity To be able to explain the oles of the fuel ods, modeato, coolant and contol ods To be able to give examples of the mateials use fo each of the above Making Electicity This is a typical nuclea fission eacto. A nuclea powe station is simila to a powe station poweed by the combustion of fossil fuels o biomass. In such a station the fuel is bunt in a boile, the heat this poduces it uses to heat wate into steam in the pipes that cove the oof and walls of the boile. This steam is used to tun a tubine which is connected to a geneato that poduces electicity (see GCSE Physics and A Unit 4). Steam entes the cooling towes whee is it condensed into wate to be used again. In a nuclea fission eacto the heat is poduced in a diffeent way. Components of a Nuclea Reacto Fuel Rods This is whee nuclea fission eactions happen. They ae made o Uanium and thee ae hundeds of them spead out in a gid like patten. Natual Uanium is a mixtue of diffeent isotope. The most common ae U 8 which accounts fo 99.8% and U 5 which accounts fo only.7% of it. 8 will only undego fission when exposed to vey high-enegy neutons whilst 5 will undego fission much moe easily. The Uanium that is used in fuel ods has a highe pecentage of 5 and is said to be eniched. This is so moe fission eactions may take place. Modeato Role: The neutons that ae given out fom nuclea fission ae tavelling too fast to cause anothe fission pocess. They ae eleased at x 7 m/s and must be slowed to x m/s, losing % of thei kinetic enegy. The neutons collide with the atoms of the modeato which tuns the kinetic enegy into heat. Neutons that ae tavelling slow enough to cause a fission pocess ae called themal neutons, this is because they have the same amount of kinetic enegy as the atoms of the modeato (about.5 ev at C). Factos affecting the choice of mateials: Must have a low mass numbe to absob moe kinetic enegy with each collision and a low tendency to absob neutons so it doesn t hinde the chain eaction. Typical mateials: gaphite and wate. Coolant Role: Heat is caied fom the modeato to the heat exchange by the coolant. The pessuise and the pump move the hot coolant to the heat exchange, hee hot coolant touches pipes caying cold wate. Heat flows fom hot coolant to cold wate tuning the wate into steam and cooling the coolant. The steam then leaves the eacto (and will tun a tubine) as the coolant etun to the eacto. Factos affecting the choice of mateials: Must be able to cay lage amounts of heat (L The Specifics), must be gas o liquid, non-coosive, non-flammable and a poo neuton absobe (less likely to become adioactive). Typical mateials: cabon dioxide and wate. Contol ods Role: Fo the eacto to tansfe enegy at a constant ate each nuclea fission eaction must lead to one moe fission eaction. Since each eaction gives out two o moe we must emove some of the exta neutons. The contol ods absob neutons, educing the amount of nuclea fission pocesses occuing and making the powe output constant. They can be loweed futhe into the fuel ods to absob moe neutons and futhe educe the amount of fission occuing. Some neutons leave the eacto without inteacting, some tavel too fast while othe ae absobed by U 8 nuclei. If we need moe neutons we can aise the contol ods. Factos affecting the choice of mateials: Ability to absob neutons and a high melting point. Typical mateials: boon and cadmium.