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1 DUAL NATURE OF MATTER AND RADIATION Photons: Electromagnetic radiation travels in the form of small packets of energy which are called photons. Important Properties of photons: i. According to quantum theory of light, radiation from any given source always travel in the form of photons. hc ii. The energy of photon is given by E h Where h is Planck s constant and its value is 6.6x0-34 Js iii. iv. Velocity of photon is equal to the velocity of light i.e. 3 x 0 8 m/s The mass of the particle varies with velocity according to the relation m0 m. Where m 0 is the rest mass of photon. As photon moves with the c / v velocity of light v=c, thus m 0=0. Hence photon has zero rest mass. h h v. Momentum of photon is given by relation, p mc c vi. Photons are electrically neutral particle and they are not deflected by the either vii. viii. electric or magnetic field. The velocity of photons in different media is different due to the change in wavelength, but the frequency of photon remains constant. Energy of a photon is usually expressed in electron volt (ev). ev =.6 x 0-9 J Free electrons in metals: In metals, the electrons in the outermost shell of the atoms are loosely bound. It is because of the small attractive force between the positive nucleus and electrons in the outermost shell. These electrons can freely move in a metal like gas molecules in a given volume of certain gas. But the electron can t leave the metal surface because of the attractive force of other positive charges. There exists a potential barrier which they must overcome before leaving the surface. To overcome that potential barrier they require certain minimum amount of energy. This minimum energy required by an electron just to escape from the metal surface so as to overcome the restraining forces is called work function. Work function is generally denoted by φ 0. Electron Emission: Electron emission is defined as the phenomenon of emission of free electrons from the metal surface. The various modes for providing energy to the electrons and making them free are [a] Thermionic emission: It is phenomenon of emission of free electrons from the metal surface when heated suitably. On heating the metal, the free electrons acquire sufficient P a g e D N M R b y U m e s h T y a g i
2 energy to overcome the restraining forces. The electrons so emitted are called thermal electrons or thermions. [b] Photoelectric emission; It is the phenomenon of emission of electrons from the metal surface when light of suitable energy falls on them. By suitable energy we mean that the energy of incident photons should be more than the work function from the metal surface. The emitted electrons are photoelectrons. [c] Field emission: The phenomenon of emission of electrons from the metal surface when strong electric field is applied across it. The electric field intensity will provide energy to the electrons and the emitted electrons are field electrons. Electric field of the order of 0 8 V/m is required for emission. [d] Secondary emission: When fast moving electrons called primary electrons are allowed to fall on the metal surface, they collide with the free electrons inside the metal surface. The energy transfer between primary electrons and electrons inside the metal surface provides electron emission from the metal surface. The emitted electrons are called secondary electrons. Photoelectric Effect- The phenomenon of emission of electrons from a metal surface when light of suitable frequency falls on it, is called photoelectric effect. The emitted electrons are called photoelectrons and the corresponding current is called photoelectric current. The suitable energy [work function] for different metals is different. Alkali metals can emit electrons even with visible light whereas metals like zinc or magnesium requires ultraviolet light. EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT The photoelectric effect was first observed in 887 by Heinrich Hertz ( ) during experiments with a spark-gap generator the earliest form of radio receiver and it was Philipp Lenard (86 947), an assistant of Hertz, who performed the earliest, definitive studies of the photoelectric effect. The experimental set is shown in the figure. The apparatus consist of an evacuated glass tube fitted with two electrodes C (emitter) and A (collector). A varying p.d. can be applied across two electrodes. The polarity of the electrodes can be reversed with the help of commutator. The frequency and intensity of light incident can also be changed. When a suitable radiation is incident on the electrode C, electrons are emitted from the surface. If the collector is at a positive potential w. r. t the emitter, the electrons are attracted by it and a current called photoelectric current flows in the circuit. P a g e D N M R b y U m e s h T y a g i
3 Effect of potential: When we increase the potential of A w.r.t. C, for a given value of intensity and frequency it was found that the photoelectric current also increases. At one particular value of accelerating voltage the photoelectric current saturates. If we increase the potential beyond this value the current will remain constant. This basically implies that all the electrons emitted by the cathode had started reaching the plate A If negative potential is applied on A relative to C, the photoelectric current decreases as electrons emitted by the cathode are repelled by the negative potential of plate C. thus, lesser number of electrons will be able to reach the plate A. It was found the photoelectric current than decreases rapidly till it reduces to zero at certain negative value of potential of plate A relative to B. This, minimum negative potential V 0, of plate A relative to B for which the photoelectric current becomes zero is called stopping potential. At this potential the electron with maximum kinetic energy will be stopped. ev mv or 0 max V mv 0 max Thus, the stopping potential gives the estimate of the maximum kinetic energy of photoelectrons. Effect of Frequency: If we take three radiations of different frequency but having the same intensity. In this case, the number of photons striking the metal surface per second per unit area will be same, thus, the photoelectric current will be same in all the three cases. But, as the frequency of photon beams is different the maximum kinetic energy of emitted photons will also be different. Larger the frequency of incident photon beam larger will be the maximum kinetic energy and larger will be the magnitude of the stopping potential. Effect of intensity: If we consider three different photon beams striking the metal surface having same frequency but different intensity [I >I >I 3], then the photoelectric current will be different in the 3 cases. Larger the intensity larger will be the photoelectric current as shown in the graph. But because the frequency of incident beam is same sopping potential for all the three beams will be equal. 3 P a g e D N M R b y U m e s h T y a g i
4 Variation of stopping potential with frequency: The stopping potential varies linearly with the frequency of incident photon beam. If frequency of photon beam is less than the threshold frequency then the stopping potential will be zero as no photoelectric current flows. But if ν > ν 0, stopping potential increases with ν. Laws of Photoelectric Effect: [a] For a given metal surface and frequency of the incident radiation, the number of photoelectrons ejected per second by the metal surface is directly proportional to the intensity of the incident light. [] For a given metal surface, there exists a minimum frequency of incident radiation below which no emission of electrons will take place. This frequency is called threshold frequency. [3] Above the threshold frequency, the maximum kinetic energy of emitted photoelectrons is independent of the intensity of incident radiation and depends only on the frequency of the incident radiation. [4] The photoelectric effect is in instantaneous phenomenon. The time lag between the photon striking the metal surface and emission of electrons is only 0-9 s Important Graphs- (a) Graph between applied potential and photoelectric current for different values of Intensity (b) Graph between intensity of light and photoelectric current i.e. photoelectrons emitted per second (rate of emission of electrons) (c)graph between threshold frequency and stopping potential (d) Graph between applied potential and photoelectric current for different values of frequency. 4 P a g e D N M R b y U m e s h T y a g i
5 Note- () The negative potential at which the current in the circuit becomes zero is called as cut-off potential or stopping potential (V 0). () The minimum frequency required to emit an electron from a metal surface is called threshold frequency FAILURE OF WAVE THEORY- The laws of photoelectric effect could not be explained on the basis of wave theory of light due to the following reasons. (i) According to wave theory, the energy carried by waves depends upon the intensity and increases with the increase in intensity. The light waves with larger intensity will provide more energy to electrons of metal; consequently the energy of electrons will increase. But according to experimental observations, the kinetic energy of photoelectrons does not depend on the intensity of incident light. (ii) (iii) According to wave theory the light of any frequency can emit electrons from metallic surface provided the intensity of light be sufficient to provide necessary energy for emission of electrons, but according to experimental observations the light of frequency less than threshold frequency can not emit electrons; whatever the intensity of incident light may be. According to wave theory the energy transferred by light waves will not go to a particular electron, but it will be distributed uniformly to all electrons present in the illuminated surface. Therefore electrons will take some time to collect the necessary energy for their emission. But experimental observations show that the emission of electrons take place instantaneously after the light is incident on the metal; whatever the intensity of light may be. EINSTEN S PHOTOELECTHIC EQUATION AND EXPLANATION OF LAW OF PHOTOELECTRIC EFFECT - To explain photoelectric effect, Einstein postulated that when a photon carrying energy h falls on a metal surface then it is completely absorbed by a single electron. Electron utilizes some amount of this energy to come out from the metal surface which is called as the work function (W) of metal and the rest amount of energy is carried by electron in the form of kinetic energy. Thus h W mvmax or mvmax h W Here, m is the mass of electron and v max is the maximum velocity of the photoelectrons. (In fact, most of the electrons possess kinetic energy less than the maximum value as they lose a part of their kinetic energy due to collisions in escaping from the metal). If ν = ν 0, then K.E. =0. 0 h W W h P a g e D N M R b y U m e s h T y a g i
6 max ( 0 ) () mv h This relation is called as the Einstein s photoelectric equation. If V 0 is the cut-off potential then above equation can also be written as- ev h( ) mv ev 0 0 max 0 Explanation of Laws of Photoelectric Effect by Einstein- From Einstein s relation, it follows that. If 0 then the kinetic energy of the photoelectrons [according to equation ()] will become negative which is not possible so no electron will be emitted from the metal surface if the frequency of the incident light is less than a certain value called as threshold frequency. Thus the frequency of incident radiation should be greater than the threshold frequency for the metal for the ejection of electrons.. Equation () shows that the photoelectrons with greater value of maximum kinetic energy will come out of the metal surface, when the frequency of incident radiation is increased. Since the equation () does not involve the term of intensity so the maximum kinetic energy does not depend upon the intensity. 3. The rate of emission of photoelectrons will be large, when intense beam of light is incident on the metal surface. This is because, an intense beam of light contains a large number of photons which transfers their energy to a larger number of electrons and hence more photoelectrons are emitted. 4. The electron is emitted from the metal surface in a time less than one nanosecond so the photoelectric effect is an instantaneous process. Graph between frequency (ν) and stopping potential (V0): As we know that h W ev0 h W or V0 So V0 e e V 0 Thus, ν-v 0 graph is a straight line as shown in adjacent figure. On comparing the above equation with straight line equation, y mx C, The slope of the straight line, m h / e and the intercept on y-axis is C W / e Graph between frequency (ν) and stopping potential (V0) : o -W/e K max ν 0 ν K h( ) So K max 0 max Comparing with y mx C Slope of straight line, m h and o ν 0 ν Intercept on y-axis, C W -W 6 P a g e D N M R b y U m e s h T y a g i
7 Photoelectric Cell: It is a device which converts light energy into the electrical energy. Photoelectric cells can be 3 types [a] Photo emissive Cell: Photo emissive cell or phototube consists of a quartz tube with semi cylindrical metal plate acting as cathode and wire loop acting as anode. The tube has insulating base with metallic pins to fix the tube in the socket. This tube is connected to the external circuit using battery and micro ammeter and a load resistance R. When light of frequency greater than the threshold frequency for the metal surface is allowed to fall on the cathode, photoelectrons are emitted. These are attracted by the positive potential on the anode loop and current begins to flow in the circuit. The photoelectric current, which flows in the circuit, is measured using micro ammeter. This current is generally very small and needs amplification before it can be used. The current flows only till the photons are falling on the metal surface. [b] Photovoltaic Cell: It consists of three layers as shown in figure. The metallic surface of copper or gold with thin semi conducting layer of cuprous oxide and a thin transparent film of silver or gold. When sunlight falls on the top transparent layer and passes through it, it illuminates the semiconducting layer. The photoelectrons are emitted by this layer and are collected by top layer. This creates a potential difference between the top two layers and conventional current begins to flow. Thus, cell supplies current without any batteries. Here also, the photoelectric current is directly proportional to the intensity of the incident light falling on the surface. [c] Photoconductive cell: Photoconductive cell has its working based on the principle that the electrical resistance of the semiconductors decreases with the increase in temperature of the semiconductor. It consists of thin transparent surface film which is placed on thin layer of selenium [semiconductor] which in turn is placed on iron layer. A potential difference is applied across the surface of the film and iron layer. When light of suitable frequency falls on the surface film, the electrical resistance of the semiconductor decreases and current begins to flow in the outer circuit, this current change with the change in intensity of the incident light. Applications of Photoelectric Cells- [] It is used as burglar alarm in houses or banks etc. [] A photocell can be used to locate flaws in the metallic sheet in industrial applications [3] It is used for automatic switching on and off of the streetlights. [4] It is used for automatic counting of number of persons entering or leaving a given hall or stadium. 7 P a g e D N M R b y U m e s h T y a g i
8 [5] It is used as fire alarm in the case of accidental fire in the building [6] Photoelectric cells are used in TV and camera for telecasting scenes by converting light and shade into electric signals. [7] Photocells are used to compare the illuminating power of two different sources of light. Dual Nature of matter: There are some phenomenon involving light like photoelectric effect, Compton scattering etc which can be explained only on the particle nature of light. Whereas, some other phenomenon like Interference, diffraction, polarization etc. can be explained on the wave nature of light. This implies that light possess both the particle as well as wave nature. Thus, light phenomenon can be classified into 3 categories i. The phenomenon like photoelectric effect or Compton scattering which can be explained using particle character ii. iii. The phenomenon like diffraction or polarization, which can be, explained only using wave character. Phenomenon like refraction or refraction, which can be, explained either by particle or wave character. De-Broglie Hypothesis {Matter Waves}- De-Broglie stated that as light possesses dual character and universe consists of matter and radiation only. As nature loves symmetry, thus matter should also possess dual nature both particle as well as a wave. According to de-broglie a wave is always associated with the moving particle which controls the particle in every aspect. This wave is called de- Broglie wave or matter wave. For a particle of mass m moving with the velocity v the de-broglie wavelength associated with the particle is given by h mv Proof: According to Plank s quantum theory, the energy associated with a photon of frequency ν is given by E h Also, according to relativistic mass formula for particle of rest mass m 0 and momentum p the energy is given by- E p c m c 4 0 As rest mass of the photon is zero, thus energy of photon becomes E pc Equating the above two values of energy, we get, h h h h pc or p or c p 8 P a g e D N M R b y U m e s h T y a g i
9 Thus, De- Broglie stated that as photon and matter particles behave in similar manner, therefore the same formula can be applied to matter particle. h p mv mv Thus, if the velocity of the particle is zero, its wavelength will be infinity and if velocity of the particle is infinity then wavelength will be zero. Note: In daily life the mass of the particle very large. Thus the de-broglie wavelength comes out to be very small. The de-broglie wavelength of any particle is independent of the charge on the particle. It was found that velocity of De-Broglie waves is always more than the velocity with which the particle moves. De-Broglie wavelength of an accelerated electron- If an electron is made to accelerate through the potential difference of V volt, then electrical potential energy of the electron gets converted into its kinetic energy i.e. Kinetic Energy of electron, K ev Also Or p K or p mk p mev m de-broglie s wavelength associated with an accelerated electron is given as h h p mev or A V V Relation for de-broglie wavelength and temperature: The average kinetic energy of a particle at absolute temperature T is given as K 3 k T, Where k B is the Boltzmann s constant B If m is the mass of particle and v is the velocity then, K mv Momentum of the particle, 3 p mv mk ) m k T 3mk T B B de-broglie wavelength h p h 3 B mk T 9 P a g e D N M R b y U m e s h T y a g i
10 DAVISSON AND GERMER S EXPERIMENT (ELECTRON DIFFRACTION): - Davisson and Germer gave the experimental demonstration of the de-broglie wave associated with the moving electron i.e. it establish the wave nature of matter. EXPERIMENTAL SET-UP: It consists of an electron gun. A fine beam of electron accelerated to a known energy strikes to a Ni- crystal. A detector, which moves on a circular scale, detects the diffracted beam and measures the angle of diffraction. WORKING: -The accelerated beam of electron strikes the nickel crystal normally. The intensity of the scattered beam is measured at different accelerating voltages for different values of (which is the angle between the incident direction and scattered direction and called the latitude angle). Polar graphs are plotted between the intensity (I) of scattered electron and the latitude angle for different accelerating voltages. From the graphs it is clear that the intensity of scattered beam is maximum for = 50 at 54 volt The glancing angle (i.e. the angle between the direction of scattered electron and crystal atomic plane) is given by I θ Electron Gun ϕ Ni Crystal θ Scattered Beam 54V Detector Φ 80 or 80 For maximum intensity θ = = 65 Now according to Bragg s law- d sin n For st order diffraction, n = and inter atomic separation for Ni- crystal, d = 0.9 A λ = 0.9 sin65 or λ =.65A Now according to de-broglie hypothesis- The wavelength of wave associated with electron accelerated to 54 volt is given by-.7.7 A.66A V 54 Thus there is a close agreement between the estimated value of de-broglie wavelength and the experimental value determined by Davisson and Germer. Thus this experiment gave a strong evidence for the de-broglie hypothesis or the wave nature of matter. 0 P a g e D N M R b y U m e s h T y a g i
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