AP Physics B - Unit 11 Notes Yockers

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1 AP Physics B - Unit 11 Notes Yockers Blackbody Radiation and Planck s Hypothesis (pp ) - an object at any temperature is known to emit electromagnetic radiation that is sometimes referred to as thermal radiation - thermally agitated charges emit radiation low temperatures infrared radiation warmer visible light high temperatures ultraviolet radiation - a blackbody is an ideal system that absorbs all radiation incident upon it - the energy radiated from a blackbody varies with wavelength and temperature Wien s displacement law T m K max 10 - max is the wavelength at which an energy curve peaks - T is the absolute temperature of the object emitting the radiation - the wavelength of electromagnetic waves radiated from an object is dependent solely on the temperature of the object

2 - Planck resonators (charged oscillators) only have certain discrete energies (ultraviolet catastrophy) E n nhf n = quantum number (positive integer) f = frequency of resonator s oscillation h = 6.66 x J s = Plank s constant - energy is quantized (the birth of quantum physics!) Photoelectric Effect and the Particle Theory of Light (pp ) - photoelectric effect when light is incident on certain metallic surfaces, electrons (photoelectrons) are emitted description of a photoelectric experiment/circuit - maximum kinetic energy of the photoelectrons is related to stopping potential by KE e max V s

3 - several features of the photoelectric effect cannot be explained with classical physics or with the wave theory of light no electrons are emitted if the incident light frequency falls below some cutoff frequency, f c, that is characteristic to the material being illuminated. This is inconsistent with the wave theory, which predicts that the photoelectric effect should occur at any frequency, provided the light intensity is sufficiently high the maximum kinetic energy of the photoelectrons is independent of light intensity. According to wave theory, light of higher intensity should carry more energy into the metal per unit time and therefore eject photoelectrons having higher kinetic energies the maximum kinetic energy of the photoelectrons increases with increasing light frequency. The wave theory predicts no relationship between photoelectron energy and incident light frequency electrons are emitted from the surface almost instantaneously (less than 10-9 s after the surface is illuminated), even at low intensities. Classically, we expect the photoelectrons to require some time to absorb some incident radiation before they acquire enough kinetic energy to escape from the metal - sketch or identify a graph of Vs versus frequency for a photoelectric experiment from such a graph determine threshold frequency and work function calculate an approximate value of h e - Einstein (Nobel Prize in 191) a tiny packet of light energy or photon would be emitted when a quantized oscillator made a jump from an energy state of E n =nhf to the next lower state E n-1 =(n-1)hf. photon discrete unit of light emitted by a resonator conservation of energy would require the decrease in oscillator energy, hf, to be equal to the photons energy, E, so hc E hf - be able to describe in units of J or ev - 1 ev = 1.60 x J the maximum kinetic energy of liberated photoelectrons is hf KE max - is called the work function of the metal which represents the minimum energy with which an electron is bound in the metal (on the order of a few ev) - with the photon theory of light, we can explain the previously mentioned features of the photoelectric effect that cannot be understood using concepts of classical physics that the effect is not observed below a certain cutoff frequency follows from the fact that the photon energy must be greater than or equal to. If the energy of the incoming photon does not satisfy this condition, the electrons are never ejected from the surface, regardless of light intensity that KE max is independent of the light intensity can be understood with the following argument. If the light intensity is doubled, the number of photons is doubled, which doubles the number of photoelectrons emitted. However, their maximum kinetic energy depends only on the light frequency and the work function, not on the light intensity that KE max increases with increasing frequency (KE max = hf - ) that the electrons are emitted almost instantaneously is consistent with the particle theory of light, in

4 which the incident energy arrives at the surface in small spatial packets and there is one-to-one interaction between photons and photoelectrons. In this interaction, the photon s energy is imparted to an electron that then has enough energy to leave the metal. This is in contrast to the wave theory, in which the incident energy is distributed uniformly over a large area of the metal surface Wave Properties of Particles (pp ) - Louis de Broglie (Nobel Prize in 199) postulated that because photons have wave ( and f) and particle (mv and E) characteristics, perhaps all forms of matter have both properties the relationship between energy and momentum for a photon is p=e/c the momentum of a photon can be expressed as E hc h p c c because the momentum of a particle of mass m and speed v is mv=p, the de Broglie wavelength of a particle is (De Broglie s hypothesis) h h p mv de Broglie postulated that the frequencies of matter waves obey the Einstein relationship E=hf, so E f h - The Davisson-Germer Experiment (p. 90) provides evidence for the wave nature of electrons description (the discovery was made by accident!) - involved the scattering of low-energy electrons ( 54eV) projected toward a nickel target in a vacuum - in one experiment the nickel target was badly oxidized because of an accidental break in the vacuum system - when the nickel target was heated in a flowing stream of hydrogen to remove the oxide coating, electrons scattered by it exhibited intensity maxima and minima at specific angles - the nickel had formed large crystal regions on heating and the regularly spaced planes of atoms in the crystalline regions served as a diffraction grating for electrons Davisson and Germer performed more extensive diffraction measurements on electrons scattered from single-crystal tagets results showed conclusively the wave nature of electrons confirmed the de Broglie relationship p h X-rays (pp ) - typical x-ray wavelengths are about 0.1 nm, which is on the order of the atomic spacing in a solid - x-rays are part of the electromagnetic spectrum frequencies higher than those of ultraviolet radiation can penetrate most materials with relative ease - x-rays are produced when high-speed electrons are suddenly decelerated when a metal target is struck by electrons that have been accelerated through a potential of several thousand volts electrons emit radiation when they undergo a deceleration inside the target - as an electron passes close to a positively charged nucleus contained in the

5 target material, it is deflected from its path because of its electrical attraction to the nucleus (deflection is due to acceleration) - classical physics shows that any charged particle will radiate energy in the form of electromagnetic radiation when it is accelerated - quantum theory dictates that the radiation will be in the form of photons - since the radiated photons carry energy, the electrons involved must have lost kinetic energy during their encounters with the target nuclei - in an extreme example when all of an electron s energy is lost in a single collision the initial energy of the electron is transformed completely into the energy of the photon hc e V hf max min and the shortest wavelength that can be produced is hc min ev - the x-ray spectrum (pp ) of a metal target consists of a broad continuous spectrum (bremsstrahlung) plus a number of sharp lines, which are due to characteristic x-rays bremsstrahlung x-radiation with its origin in the slowing down of electrons (braking radiation) characteristic x-rays - a bombarding electron collides with a target atom and has sufficient energy to remove an inner-shell electron from the atom - the vacancy created in the shell is filled when an electron in a higher level drops down into the level containing the vacancy - this transition is accompanied by the emission of a photon whose energy equals the difference in energy between the two levels detailed x-ray spectra Compton Scattering Arthur Compton (p ) - further justification for the photon theory of light - description of the experiment x-ray beam of wavelength 0 directed toward a block of graphite scattered x-rays had a slightly longer wavelength,, than the incident x-rays (lower energy) remember, both energy and momentum must be conserved

6 - Compton shift formula h 1 m c 0 e cos h is known as the Compton wavelength and has a value of nm mec the Compton shift depends on the scattering angle,, and not on wavelength Atomic Spectra (pp ) - when an evacuated glass tube is filled with a gas at very low pressure with a potential difference applied between metal electrodes in the tube great enough to produce an electric current in the gas, the tube emits light whose color is characteristic of the gas in the tube - when the emitted light is analyzed with a spectrometer a series of discrete lines are observed (emission spectrum) each line corresponds to a different wavelength (color) of light - the wavelengths contained in a given line spectrum are characteristic of the element emitting the light - because no two elements emit the same line spectrum, this phenomenon provides a technique for identifying elements in a substance - an element can also absorb light at specific wavelengths with corresponding spectral lines giving an absorption spectrum an absorption spectrum is obtained by passing a continuous radiation spectrum through a vapor of the element being analyzed the absorption spectrum consists of a series of dark lines superimposed on the

7 otherwise continuous spectrum each line in the absorption spectrum of a given element coincides with a line in the emission spectrum of the element - radiation is emitted by an atom when an electron jumps from a more energetic initial state to a lower state frequency of the emitted radiation is E E hf i to emit radiation f E E i f - energy incident upon an atom causes an electron to jump from a lower energy state to a more energetic state energy is absorbed by the atom excited atoms quickly fall to lower energy state this emits radiation as described above - to determine the wavelength of emitted radiation R H n f n i the Rydberg constant R H = x 10 7 m -1 n has integral values corresponding to energy levels - to determine the energies of the quantum levels (for hydrogen) 13.6 E n n ev - the minimum energy required to ionize the atom (to completely remove the electron in hydrogen, for example) is called the ionization energy - in the diagram above, the uppermost level shown, corresponding to n, represents the state for which an electron is completely removed the ionization energy for hydrogen is 13.6 ev the wavelength required to ionize an atom can be determined by using the equations above for wavelength or frequency (and the conversion from J to ev) - the various series in the hydrogen spectrum Paschen series infrared Balmer series visible

8 Lyman series ultraviolet - example The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number n=, as shown above. (a) Find the longestwavelength photon emitted in the Balmer series and determine its frequency and energy. (b) Find the shortest-wavelength photon emitted in the same series E E i f hf n f n i RH Properties of Nuclei (p ) - nucleons protons neutrons - symbols mass number (A) = the number of nucleons in the nucleus neutron number (N) = number of neutrons in the nucleus atomic number (Z) = number of protons in the nucleus A Z X is the symbol used to represent nuclei - X represents the chemical symbol for the element - isotopes of an element have the same Z value but different N and A values - charge and mass (p. 940) charge of a proton = +e charge of an electron = -e neutrons are electrically neutral E n n ev - nuclear stability (p. 94) the nuclear force the very large repulsive electrostatic forces between protons should cause the

9 nucleus to fly apart nuclei are stable because of the presence of a short-range force nuclear force - acts over distances of about fm (f = femto ) - acts between all nuclear particles neutron-neutron proton-neutron proton-proton - protons attract each other via the nuclear force and at the same time repel each other through the Coulomb force - nuclear force dominates the Coulomb repulsive force within the nucleus (at short ranges) - the nuclear forces associated with neutron-neutron, proton-neutron, and proton proton interactions are approximately the same apart from the additional repulsive Coulomb force for the proton-proton interaction - the decay processes (pp ) radioactive nuclei spontaneously decay via alpha, beta, and gamma decay alpha decay - if a nucleus emits an alpha particle 4 He it loses two protons and two neutrons N decreases by Z decreases by A decreases by 4 A A 4 4 X Z Z YHe X is called the parent nucleus Y is the daughter nucleus - examples U Th He Ra Rn 4 He beta decay the daughter nucleus has the same number of nucleons as the parent nucleus, but the atomic number is changed by 1 A A Z XZ 1Y e (e + is a positron antiparticle of an electron) A A Z XZ 1Y e - nucleon number and total charge are conserved 14 - example: C 14 Y 6 7 e - where did the electron come from (this is the nucleus)? the emitted electron is created in the nucleus by a process in which a 1 neutron is transformed into a proton n 1 p 0 1 e - beta decay posed a problem because it appeared to violate the conservation of

10 energy and momentum a third particle must be present to carry away the missing energy and to conserve momentum the neutrino was finally discovered in no electric charge - mass smaller than an electron (possibly zero!) - has spin - weak interactions with matter hard to detect - correct equations with the addition of neutrinos A Z X A Z1 Y e A A Z XZ 1Y e - in beta decay, an electron and an antineutrino are emitted or a positron and a neutrino gamma decay - a nucleus may reach an excited state as the result of a violent collision with another particle - more common for a nucleus to be in an excited state as a result of alpha or beta decay - gamma decay is a second decay for the excited nucleus to reach a lower energy state by emitting one or more photons (similar to the emission of light by an atom) photons emitted are gamma rays gamma rays have very high energy relative to the energy of visible light - example 1 1 * B C 5 6 e 1 * 1 6 C 6 C the * indicates that the carbon nucleus is left in an excited state following the decay - gamma emission does not result in any change in either Z or A - nuclear fission (p ) occurs when a heavy nucleus splits, or fissions, into two smaller nuclei the total mass of the products is less than the original mass of the heavy nucleus 35 the fission of U by slow (low energy) neutrons can be represented by the reaction * n U U X Y neutrons X and Y are known as fission fragments the U nucleus captures a thermal (slow-moving) neutron * - the capture results in the formation of 36 U, and the excess energy of this nucleus causes it to undergo violent oscillations * - the 36 U nucleus becomes highly distorted, and the force of repulsion between protons in the two halves of the dumbbell shape tends to increase the distortion - the nucleus splits into two fragments, emitting several neutrons in the process typical reaction of this type is n U Ba Kr 3 n

11 - the fission fragments, barium and krypton (in above example), and the released neutrons have a great deal of kinetic energy - the amount of energy released is (8. 7.) MeV per fission event, so if we assume a total of 40 nucleons MeV MeV Q 40 nucleons MeV nucleon nucleon Q is the disintegration energy for a fission process - using E mc to calculate energy released in nuclear processes example C atom N atom C has a mass of u and 7 N has a mass of m u - this corresponds to an energy release of E m c u 931 MeV u E c c MeV mc u kg u m s.5110 J 931 MeV u 931 MeV c u m s -7 kg -19 J u ev

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