DUAL NATURE OF RADIATION AND MATTER

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1 DUAL NATURE OF RADIATION AND MATTER November 24, 2008 ELECTRON EMISSION Free electrons are responsible for their conductivity. However, the free electrons cannot normally escape out of the metal surface. If an electron attempts to come out of the metal, the metal surface acquires a positive charge and pulls the electron back to the metal. The free electron is thus held inside the metal surface by the attractive forces of the ions. WORK FUNCTION(φ o ) A certain minimum amount of energy has to be given to an electron to pull it out from the surface of the metal. This minimum energy required by an electron to escape from the metal surface is called the work function of the metal.the work function φ o depends on:- The property of the material The nature of the surface Units used to express work function(φ o ):Work function is measured in units of energy but electron volt(ev )(One electron volt is the energy gained by an electron when it has been accelerated by a potential difference of 1 volt), is preferred to joules. 1eV = J The minimum energy required for the electron emission from the metal surface can be supplied to the free electrons by any one of the following physical processes: Thermionic emission: By suitably heating, sufficient thermal energy can be imparted to the free electrons to enable them to come out of the metal. Field emission: By applying a very strong electric field (of the order of 10 8 V m 1 ) to a metal, electrons can be pulled out of the metal, as in a spark plug(used in automobiles). Photo-electric emission: When light of suitable frequency illuminates a metal surface, electrons are emitted from the metal surface. These photo(light)-generated electrons are called photoelectrons. PHOTOELECTRIC EFFECT Photo electric effect involves the conversion of light energy into electrical energy. 1

2 When light falls on a metal surface, some electrons near the surface absorb enough energy from the incident radiation to overcome the attraction of the positive ions in the material of the surface. After gaining sufficient energy from the incident light, the electrons escape from the surface of the metal into the surrounding space. EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT Experimental arrangement Figure 1 depicts a schematic view of the arrangement used for the experimental study of the photoelectric effect. It consists of an evacuated glass/quartz tube having a photosensitive plate C and another metal plate A. Monochromatic light(single wavelength) from the source S of sufficiently short wavelength passes through the window W and falls on the photosensitive plate C (emitter). Figure 1: Expt arrangementfor the study of Photo Electric effect The electrons that are emitted (due to photo electric emission) by the plate C and are collected by the plate A (collector). The battery maintains the potential difference between the plates C and A, that can be varied. The polarity of the plates C and A can be reversed by a commutator. Thus, the plate A can be maintained at a desired positive or negative potential with respect to emitter C Voltmeter V measures the potential difference between the anode and the cathode,the Ammeter measures the photo current circuit(µa). This experimental arrangement is used to study the variation of photo current with (a)intensity (b) Potential Difference (c) frequency (d) The nature of the plate C Effect of intensity of light on photocurrent The collector(a) is maintained at a positive potential with respect to the cathode(this is done by connecting terminals 2 with 3 and terminals 5 with 6 in the figure refer 1) The frequency of the incident radiation is kept constant The potential difference V between the plates A and C is kept constant. 2

3 The Intensity of the light varied and the resulting photo current measured. RESULT It is found that when the intensity of light is increased the photo current also increases linearly. Figure 2: Variation of photo current with light intensity INFERANCE: The photocurrent is directly proportional to the number of photoelectrons emitted per second. This implies that the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.as per the particle theory of light as the intensity of light is increased the number of photons emitted per second increases but the energy of each the photon remains the same,since more photons will release more electrons the current will increase with intensity. Effect of potential on photoelectric current The intensity of the incident light(i) is kept constant(for a given variation in potential difference) The frequency of the light is kept constant. The potential difference between the plates is varied. Experiment Part I The cathode C is illuminated with light of frequency ν and intensity I 1.The anode A is maintained at some positive potential with respect to C and the positive potential of A is gradually varied and the resulting photo current measured. Result:when the positive potential of A is increased the photo current increases until at one stage even if the anode potential is increased there is no increase in the photo current or in other words the photo current reaches a maximum and saturates,this maximum value of photo current is called saturation current The saturation current corresponds to the state at which all the electrons emitted by the cathode reach the anode. Experiment Part II A negative (retarding) potential is applied to the plate A with respect to the plate C[this is done by connecting terminals 5 with 6 and 3 with 4] and make it increasingly negative gradually. 3

4 with the polarity is reversed(a being negative), the electrons are repelled and only the most energetic electrons are able to reach the collector A. We can now repeat this experiment with incident radiation of the same frequency but of higher intensity (I 3 > I 2 > I 1 ). OBSERVATIONS The photocurrent is found to decrease rapidly until it drops to zero at a certain sharply defined, critical value of the negative potential V o on the plate A called the Stopping potential. The saturation currents(the maximum photo current) are more for higher intensities. This shows that more electrons are being emitted per second, proportional to the intensity of incident radiation. But the stopping potential remains the same as shown graphically in 3 Fig.3 The minimum negative (retarding) potential V o (given to the plate A) for which the photocurrent stops or becomes zero is called the cut-off or stopping potential. The Variation of photocurrent with collector plate potential for different intensity of incident radiation is shown-note that V o is the same for all intensities. Figure 3: Variation of photocurrent with potential for differant intensities-note V o is same for all intensities INFERANCE 1. All the photoelectrons emitted from the metal do not have the same energy. 2. Photoelectric current is zero(i.e none of the photo electrons reach the plate A) when the stopping potential is sufficient to repel even the most energetic photoelectrons, with the maximum kinetic energy (KE max ),hence KE max = ev o (1) 3. For a given frequency of the incident radiation, the stopping potential is independent of its intensity. In other words, the maximum kinetic energy of photoelectrons depends on the emitter plate material, but is independent of intensity of incident 4

Effect of frequency of incident radiation on stopping potential The intensity of the incident light(i) is kept constant The frequency of the light is varied and the stopping potential is measured for

5 Effect of frequency of incident radiation on stopping potential The intensity of the incident light(i) is kept constant The frequency of the light is varied and the stopping potential is measured for different frequencies by varying the potential difference between A and C. The results are shown graphically below:- Figure 4: Variation of photoelectric current with collector plate potential for different frequencies RESULTS The graph shows that the stopping potentials V o1, V o2, V o3 more for higher frequencies(i.e more negative) The saturation current remains the same for different frequencies INFERANCE 1. Since the stopping potential increases with frequency the kinetic energy increases with frequency(because KE max = ev o )i.e at higher frequencies the kinetic energy of the electron is more hence greater retarding potential is required to stop the electron from reaching A 2. The maximum kinetic energy of the electron increases with frequency of the incident radiation but is independent of the intensity. Variation of Photoelectric with nature of material/threshold frequency ν 0 If a graph is plotted between frequency and stopping potential is plotted for different metals a straight line graph results as shown in Fig.5:- The graph shows that: Figure 5: Variation of stopping potential with frequency of incident radiation for photosensitive materials A and B. 5

6 The stopping potential V o varies linearly with the frequency of incident radiation for a given photosensitive material. The maximum kinetic energy of the photoelectrons varies linearly with the frequency of incident radiation, but is independent of its intensity. For a frequency ν of incident radiation, lower than the cut-off frequency ν 0, no photoelectric emission is possible even if the intensity is large.this minimum cut off frequency is called the threshold frequency. Threshold frequency is different for different materials if the frequency exceeds the threshold frequency(ν o ) then the photo electric emission starts almost instantaneously LAWS OF PHOTO ELECTRIC EMISSION(SUMMARY OF THE PHOTO ELECTRIC EXPER- IMENT) 1. For a given photosensitive material and frequency of incident radiation (above the threshold frequency), the photoelectric current is directly proportional to the intensity of incident light (Fig.2). 2. For a given photosensitive material and frequency of incident radiation,saturation current is found to be proportional to the intensity of incident radiation whereas the stopping potential(hence the kinetic Energy is independent of its intensity)(fig.3 ). 3. For a given photosensitive material, there exists a certain minimum cut-off frequency of the incident radiation, called the threshold frequency, below which no emission of photoelectrons takes place, no matter how intense the incident light is. Above the threshold frequency, the stopping potential or equivalently the maximum kinetic energy (KE max = ev o )of the emitted photoelectrons increases linearly with the frequency of the incident radiation, but is independent of its intensity (Fig.5). 4. The photoelectric emission is an instantaneous process without any apparent time lag (nano seconds(10 9 ) or less), even when the incident radiation is weak in intensity(dim) EINSTEINS PHOTOELECTRIC EQUATION All photo electric phenomenon(as described in the photo electric experiments) can be explained by using the Einsteins Photo electric equation. The Einsteins photo electric equation is based on the principle that radiation energy is built up of discrete units called quanta of radiation.each quanta of radiation has an energy give by E = hν where h is the Planck s constant and ν the frequency of the incident radiation.the absorption of radiation does not take place continuously but in discrete units of energy called quanta. In photoelectric effect, an electron absorbs a quantum of energy (hν) of radiation. If this quantum of energy absorbed exceeds the minimum energy needed for the electron to escape from the metal surface (work function φ 0 ),if hν is the energy of the photon which is incident 6

7 on the photo sensitive material,part of this energy is used to overcome the work function(φ 0 ) and part of it is used to provide the kinetic energy to the electron hence hν = φ 0 + KE max the electron is emitted with maximum kinetic energy(ke max ) given by KE max = hν φ 0 (2) This is known as the EINSTEIN S PHOTOELECTRIC EQUATION This equation comes from the Conservation of energy if the incident radiation has an energy hν part of it is used to over come the work function(φ o )[or to pull the electron out of the metal].the rest of the energy (hν φ o )appears as the kinetic energy of the electron(ke). Einsteins PE equation in terms of ν o and V o From equan no.1 we know that: KE max = ev o using this in the Einsteins PE equation we get ev o = hν φ 0 (3) but KE max = 1 2 mv 2 max KE max = 1 2 mv 2 max = ev o = hν φ 0 (4) Where V max is the speed of the fastest electron(all electrons don t travel with the same speed) when the frequency of the incident light is ν o the threshold frequency,then the electrons are just liberated and the kinetic energy of the electrons is 0 hence when ν = ν o, KE max = 0 0 = hν o φ o φ o = hν o (5) hence Einsteins photo electric equation can be written as(using equation 5) the above equation can be written as 1 2 mv 2 max = hν hν o = h(ν ν o ) ev o = hν hν o hence V o = hν e hν o (6) e Finding Planck s Constant The above equation shows that the graph between stopping potential V o and frequency ν will be a straight line with the y intercept being hνo.(the equation for straight line is of the form y = mx+c e where c is the y intercept),in this case y is V o,ν is x and the slope(m) is h.thus by finding the slope e of the above equation and substituting the value of e, h can be found. the graphical representation is shown in fig. 6 7

8 Figure 6: graph of frequency(ν) Vs stopping potential(v o ) Explanation of the photo electric effect experiment results using the Einsteins photo Electric Equation Explanation for the Intensity Vs Photo current Graph Fig.2:-If the intensity of the incident light is increased the number of photons increases (because the intensity of radiation is proportional to the number of energy quanta (photons)emitted/unit area/unit time) and hence greater the number of electrons emitted and therefore a proportional increase in the photo current ( cause I = q/t = ne/t) Why saturation current remains constant? and why does the stopping potential increase with frequency?(graph:fig 5):-Greater the frequency greater is the energy of the incident photons( cause E = hν)and greater is the energy of the electrons (using EINSTEINS PHOTO ELECTRIC EQUATION-KE max = hν φ o )hence a greater potential is required to stop the electrons.thus as frequency ν(ν > ν o ) increases the stopping potential increases. SATURATION CURRENT:An increase in frequency increases the energy of the incident radiation but it does not increase the no of photo electrons hence the current is not affected by the frequency of the incident light hence the saturation current remains the same(constant). REASON FOR THRESHOLD FREQUENCY:If the frequency ν of the incident radiation is less than the threshold frequency (ν o )the as per Einsteins photo electric equation(ke max = hν φ o ) the kinetic energy will be negative which is not possible hence for photo electric emission the incident frequency(ν)should be greater than the threshold frequency(ν o ) FAILURE OF WAVE THEORY: The phenomena of interference, diffraction and polarisation were explained in a natural and satisfactory way by the wave picture of light.according to this picture, light is an electromagnetic wave consisting of electric and magnetic fields with continuous distribution of energy over the region of space over which the wave is extended,but the wave picture of light could not explain the observations on photoelectric effect for the following reasons:- 1. According to the wave picture of light, the free electrons at the surface of the metal (over which the beam of radiation falls) absorb the radiant energy continuously. The greater the intensity of radiation, the greater are the amplitude of electric and magnetic fields. Consequently, 8

9 the greater the intensity, the greater should be the energy absorbed by each electron.in this picture, the maximum kinetic energy of the photoelectrons on the surface is then expected to increase with increase in intensity. Also, no matter what the frequency of radiation is, a sufficiently intense beam of radiation (over sufficient time) should be able to impart enough energy to the electrons, so that they exceed the minimum energy needed to escape from the metal surface. A threshold frequency, therefore, should not exist.these expectations of the wave theory directly contradict observations 2. In the wave picture, the absorption of energy by electron takes place continuously over the entire wavefront of the radiation. Since a large number of electrons absorb energy,the energy absorbed per electron per unit time turns out to be small,hence it should take hours or more for a single electron to pick up sufficient energy to overcome the work function and come out of the metal. This conclusion is again in striking contrast to observation that the photoelectric emission is instantaneous(in nano seconds). In short,the wave picture is unable to explain the most basic features of photoelectric emission. PHOTONS SOME PROPERTIES In interaction of radiation with matter, radiation behaves as if it is made up of particles called photons. Each photon has energy E (E = hν) and momentum p = hν/c, and speed c, the speed of light. By increasing the intensity of light of given wavelength, there is only an increase in the number of photons per second crossing a given area, with each photon having the same energy. Thus, photon energy is independent of intensity of radiation. Photons are electrically neutral and are not deflected by electric and magnetic fields. In a photon-particle collision (such as photon-electron collision), the total energy and total momentum are conserved. However, the number of photons may not be conserved in a collision. The photon may be absorbed or a new photon may be created. WAVE NATURE OF MATTER(MATTER WAVES) The study of photo electric effect brings in the dual nature of electromagnetic waves,for it shows that only using the particle theory of light photo electric can be explained,whereas phenomenon like interference,diffraction,reflection,etc can be explained using the wave nature i.e light or E.M.Waves exhibit the property of duality. Louis Victor de Broglie put forward the hypothesis that moving particles of matter should display wave-like properties under suitable conditions. De Broglie proposed that the wave length λ associated with a particle of momentum p is given as λ = h p = h mv (7) note: λ is wave property and momentum P is a property of particles. A photons energy is given by E = hν and as per Einsteins mass energy equivalence E = mc 2 9

10 equating both we get as ν = c/λ and p = mc we get hν = mc 2 λ = h p in general λ = h here λ is called the wave length of matter waves mv note:-for heavier objects wavelength is so small that it is beyond any measurement. This is the reason why macroscopic objects in our daily life do not show wave-like properties. On the other hand, in the sub-atomic domain, the wave character of particles is significant and measurable. MATTER WAVES AND HISENBERG S UNCERTAINTY PRINCIPLE According to this principle, it is not possible to measure both the position and momentum of an electron (or any other particle) at the same time exactly. There is always some uncertainty ( x)in the specification of position and some uncertainty ( p) in the specification of momentum. The product of x and p is of the order of h/2π i.e., P X h 2π The meaning of this equation is that both momentum and position of a particle cannot be determined precisely i.e if P is the error in the determination of momentum and if X is the error in the determination of position the for P to be 0 X has to be infinity [ P = 0 = (h/2π)/α]i.e the error in position is infinite if both are non zero then their minimum(so equal to sign) error can be determined using P X = h 2π If an electron has a definite momentum p, (i.e. p = 0), by the de Broglie relation, it has a definite wavelength lambda. A wave of definite (single) wavelength extends all over space. By Born s probability interpretation this means that the electron is not located in any finite region of space. That is, its position uncertainty is infinite, which is consistent with the uncertainty principle. In general, the position or the momentum of a particle can only be specified in terms of probability. de BROGLIE WAVE LENGTH OF AN ELECTRON ACCELERATED BY A PO- TENTIAL V Consider an electron (mass m, charge e) accelerated from rest through a potential V. The kinetic energy KE of the electron equals the work done (ev ) on it by the electric field: from debroglie s equation λ = h/mv ev = 1 2 mv2 v = λ = h mv = h m 2eV m 2eV m = h 2meV (8) DAVISSON AND GERMER EXPERIMENT The wave nature of electrons was first experimentally verified by this experiment 10

11 PRINCIPLE:If an electron is accelerated by an electric field then as per the de Broglie hypothesis it should have a wave length of λ = h 2meV This wavelength is verified using the principles of diffraction(which is wave phenomenon) EXPERIMENTAL ARRANGEMENT:The experimental arrangement used by is schematically shown in Fig. 7 It consists of an electron gun which comprises of a tungsten filament F, coated with barium oxide and heated by a low voltage power supply (L.T. or battery). Electrons emitted by the filament are accelerated to a desired velocity by applying suitable potential/voltage from a high voltage power supply (H.T. or battery). They are made to pass through a cylinder with fine holes along its axis, producing a fine collimated beam. The beam is made to fall on the surface of a nickel crystal. The electrons are scattered in all directions by the atoms of the crystal. The intensity of the electron beam, scattered in a given direction, is measured by the electron detector (collector). The detector can be moved on a circular scale and is connected to a sensitive galvanometer, which records the current. The deflection of the galvanometer is proportional to the intensity of the electron beam entering the collector. The apparatus is enclosed in an evacuated chamber. WORKING:By moving the detector on the circular scale at different positions, the intensity of Figure 7: Davisson Germer Experiment the scattered electron beam is measured for different values of angle of scattering θ which is the angle between the incident and the scattered electron beams. The variation of the intensity (I ) of the scattered electrons with the angle of scattering θ is obtained for different accelerating voltages. OBSERVATION AND INFERANCE:The experiment was performed by varying the accelarating voltage from 44 V to 68 V. It was noticed that a strong peak appeared in the intensity (I ) of the scattered electron for an accelarating voltage of 54V at scattering angle θ = 50 o The appearance of the peak in a particular direction is due to the constructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystals. From the electron diffraction measurements, the wavelength of matter waves was found to be 0.165nm. The de Broglie wavelength λ associated with electrons, using Eq.λ = is an excellent agreement between the theoretical value and the experimentally obtained value of de Broglie wavelength. Davisson-Germer experiment thus confirms the wave nature of electrons and the de Broglie relation. Application of Photo electric effect h 2meV, for V = 54 V was found to be 0.167nm.Thus, there 11

12 1. Used in photo cells(it is a device used to convert light energy into electrical energy) 2. In Cameras 3. Cinemotagraphy End 12

DUAL NATURE OF RADIATION AND MATTER I K GOGIA KV JHARODA KALAN DELHI.

DUAL NATURE OF RADIATION AND MATTER AIM: The aim of present self- learning module is to train the minds of the learners in building the concepts by learning on their own. The module is designed to Achieve