Title SP-5_Ch-26_Dual Nature of Radiation and Matter.pdf ✅

Chapter Contents Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Introduction Electron Emission Photoelectric Effect Einstein’s Photoelectric Equation : Energy Quantum of Radiation Particle Nature of Light : The Photon Compton Effect Wave Nature of Matter Davisson and Germer Experiment for Wave Nature of Electron Introduction Various phenomena like interference, diffraction and polarisation of light were explained by the wave nature of light. Photoelectric effect by Hertz, Compton effect by Compton, Stark effect by Stark were discovered in 20th century and were explained by quantum theory of light. According to which, the light consists of the packets of energy. Each packet of energy is called photon or quantum of light          hc E h , where h is Planck’s constant, Hence, it was concluded that light is of dual nature as some phenomena were explained by wave theory of light and some by particle nature of light, In this unit, we shall study dual nature of radiation and matter. ELECTRON EMISSION The phenomenon of emission of electrons from the metal surface is called electron emission. Work Function : To pull out electron from the surface of the metal, a certain minimum amount of energy is required. This minimum energy required by the electron is called the work function of the metal. Work function is generally denoted by 0 and it depends on the properties of the metal and nature of its surface. It is very sensitive to surface impurities. The required minimum energy for the electron emission from the metal surface can be supplied to the free electrons by the following physical process : (i) Thermionic emission : The process of emission of electrons when a metal is heated is known as thermionic emission. Chapter 26 Dual Nature of Radiation and Matter
42 Dual Nature of Radiation and Matter NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 (ii) Field emission : The process of emission of free electrons when a strong electric field ( 108 V/m) is applied across the metal surface is known as field emission. (iii) Photoelectric emission : The process of emission of electrons when light of suitable frequency is incident on a metal surface is known as photoelectric emission. (iv) Secondary emission : The process of emission of free electrons when highly energetic electron beam is incident on a metal surface is called secondary emission. The electrons so emitted are called secondary electrons. PHOTOELECTRIC EFFECT The phenomenon of emission of electrons from (preferably) metal surface exposed to light energy of suitable frequency is known as photoelectric effect. The emitted electrons are called photo electrons and the current so produced is called photoelectric current. Experimental Study of Photoelectric Effect The experimental set-up to study photoelectric effect is shown in figure. V S Quartz window Photosensitive plate Evacuated glass tube Commutator Electrons C A A Fig. : Experimental arrangement for study of photoelectric effect. To study the variation of photocurrent with (a) intensity of radiation (b) frequency of incident radiation (c) the potential difference between the plates A and C, and (d) the nature of the material of plate C, the experimental arrangement of above figure is used. To get different frequency of light falling on the emitter C, suitable-coloured filter or coloured glass is used. The change in distance of light source from the emitter varies the intensity of light. Effect of Intensity of Light on Photocurrent To attract ejected electrons from C towards collector A, the collector A is maintained at a positive potential with respect to emitter C. The intensity of light is varied, keeping the frequency of the incident radiation and the accelerating potential fixed and the resulting photoelectric current is measured each time. It is observed that the photocurrent increases linearly with intensity of incident light as shown in the figure. Photoelectric current Intensity of light Fig.: Variation of Photoelectric current with intensity of light.
NEET Dual Nature of Radiation and Matter 43 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Effect of Potential on Photoelectric Current Illuminate the plate C with radiation of fixed frequency (greater than threshold frequency) and fixed intensity, keeping the plate A at some accelerating positive potential with respect to plate C. Now we gradually vary the positive potential of plate A and measure the resulting photocurrent each time. For fixed frequency and fixed intensity of incident light, this photoelectric current increases with the increase in applied positive potential of plate ‘A’. The photoelectric current has the maximum value, when all the photoelectrons emitted by electrode ‘C’ reach the plate ‘A’. This maximum current is known as saturation current. Further increase in accelerating potential of plate A does not increase the current. When the polarity is reversed (meaning applying a negative (retarding) potential to the plate A with respect to the plate C) and increase retarding potential gradually, then electrons are repelled. The photocurrent is found to decrease rapidly and at a certain, sharply defined critical value of the negative potential V0 on the plate A, it drops to zero. The minimum negative (retarding) potential V0 given to the plate A, for a particular frequency of incident radiation, for which the photocurrent stops or becomes zero is called the cut-off or stopping potential. At this stage photo electrons of maximum kinetic energy (the fastest photoelectron) cannot reach the plate A, therefore Kmax = eV0 (Kmax is maximum kinetic energy of photoelectron) When we repeat this experiment with different intensity I 1, I 2 and I 3 (I 3 > I 2 > I 1) of incident radiation and of the same frequency, we observe that the saturation currents have reached to higher values which implies that more electrons are emitted in a unit time, proportional to the intensity of incident radiation but there is no change in stopping potential for a given frequency of the incident radiation, graphically shown in figure. Photocurrent Stopping potential –V0 O III 321 > > I3 I2 I1 Retarding potential Collector plate potential Fig.: Variation of photocurrent with collector plate potential for different intensity of incident radiation. Effect of Frequency of Incident Radiation on Stopping Potential We now study the relation between stopping potential V0 and the frequency  of the incident radiation. The resulting variation of photocurrent with collector plate potential for same intensity of light radiation at various frequencies is shown in figure. Photoelectric current Saturation current 3 >   2 1 > 3 2 1 –V03 –V02 –V01 O Collector plate potential Retarding potential Fig.: Variation of photoelectric current with collector plate potential for different frequencies of incident radiation. From graph it is clear that, greater the frequency of incident light, greater is the maximum kinetic energy of photoelectrons.
44 Dual Nature of Radiation and Matter NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 We get a straight line if we plot a graph between the frequency of incident radiation and stopping potential for different metals as shown in figure.  > 0 0 0   0 > 0 Metal A Metal B Stopping potential ( ) V0 Frequency of incident radiation ( )  Fig.: Variation of stopping potential V0 with frequency  of incident radiation for a given photosensitive material. Laws of Photoelectric Emission On the basis of experiment following conclusion can be drawn. (i) The photoelectric current is directly proportional to the intensity of incident radiation (above the threshold frequency) for a given photosensitive material and frequency of incident radiation. (ii) Saturation current is found to be proportional to the intensity of incident radiation whereas the stopping potential is independent of its intensity for a given photosensitive material and incident radiation. (iii) There exists a certain minimum cut-off frequency, called threshold frequency of the incident radiation below which no emission takes place for a given photosensitive material irrespective of intensity of the incident radiation. The maximum kinetic energy or equivalently stopping potential above the threshold frequency of the emitted photo electrons increases linearly with the frequency of the incident radiation but is not a function of intensity. (iv) The photoelectric emission is an instantaneous process. The time lag is very small between the incidence of radiation and emission of photo electrons (~10–9 s or less), even when the incident radiation is extremely dim. EINSTEIN’S PHOTOELECTRIC EQUATION: ENERGY QUANTUM OF RADIATION In photoelectric effect, an electron absorbs a quantum of energy (h) of radiation. If this absorbed energy exceeds the minimum energy (work function 0 of the metal), the most loosely bound electron will emerge with maximum kinetic energy, more tightly bound electron will emerge with kinetic energies less than the maximum value. Einstein’s photoelectric equation, Kmax = h – 0 Above equation explains all the observations on photoelectric effect. Kmax is independent of intensity of radiation but depends linearly on  Photoelectric emission is possible only if h > 0 because Kmax must be non-negative. h > 0 0 h      > 0 where 0 0 h    0 is threshold frequency. No photoelectric emission is possible below 0, even if the incident radiation of high intensity and long duration falls on the surface.