1© Manhattan Press (H.K.) Ltd Photoelectric effect Investigation of photoelectric effect Explanation of photoelectric effect by quantum theory Types of photocells

2 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 136) Photoelectric effect The photoelectric effect is the ejection of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency falls on it. Go to More to Know 1 More to Know 1

3 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 137) Investigation of photoelectric effect 1. Negative charged electroscope - divergence of gold leaf decreases - electroscope loses its -ve charges through the emission of electrons due to photoelectric effect

4 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 137) Investigation of photoelectric effect 2. With a glass plate - divergence of gold leaf remains unchanged - UV is absorbed by glass plate - only light whose f is lower than that of UV is incident on zinc plate - no electrons are emitted - only radiation of sufficiently high f is able to eject electrons from zinc surface

5 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 137) Investigation of photoelectric effect 3. Positive charged electroscope - divergence of gold leaf remains unchanged - electrons emitted from zinc surface are attracted back by +ve charges on electroscope

6 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 138) Explanation of photoelectric effect by quantum theory Photocell – used to investigate photoelectric effect

7 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 138) Explanation of photoelectric effect by quantum theory Increase p.d. across photocell When photocell is reverse bias (potential of anode), I p passes through photocell - I p is increased with p.d. When photocell is forward bias, I p is constant.

8 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 139) Explanation of photoelectric effect by quantum theory 1. Existence of threshold frequency - photoelectrons are only emitted from metal surface if f of incident radiation > threshold frequency (f 0 ) The threshold frequency (f o ) is defined as the minimum frequency of the incident radiation required causing the emission of photoelectrons from the metal surface.

9 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 140) Explanation of photoelectric effect by quantum theory 1. Existence of threshold frequency (a) By quantum theory - energy of one photon is given to one electron - if energy (hf) > , electron is emitted  = hf 0 (b) By wave theory (cannot explain it) - energy of incident radiation depends on its intensity Go to More to Know 2 More to Know 2

10 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 140) Explanation of photoelectric effect by quantum theory 2. Instantaneous emission of photoelectrons - photoelectrons are emitted as soon as radiation of sufficiently high f falls on metal surface - this happens even if intensity of radiation is low (a) By quantum theory - E = hf does not depend on intensity - energy of one photo (hf) > , electron would be emitted instantaneously

11 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 140) Explanation of photoelectric effect by quantum theory 2. Instantaneous emission of photoelectrons (b) By wave theory (cannot explain it) - energy from incident radiation would be continuously supplied to electron - electron would take some time to accumulate sufficient energy to make it escape from metal surface - the emission of photoelectron would not be instantaneous

12 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 141) Explanation of photoelectric effect by quantum theory 3. Photoelectric current directly proportional to intensity of radiation Note: The figure on the right indicates that the photoelectric current is directly proportional to the intensity of radiation.

13 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 141) Explanation of photoelectric effect by quantum theory 3. Photoelectric current directly proportional to intensity of radiation (a) By quantum theory - when the intensity of radiation is increased, no. of photons incident on metal surface increases - more free electrons in metal receive sufficient energy to escape - Rate of emission of photoelectrons increases and larger current flows

14 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 141) Explanation of photoelectric effect by quantum theory 3. Photoelectric current directly proportional to intensity of radiation (a) By quantum theory Note: The increase in the photoelectric current is due to the higher rate of emission of photoelectrons and not because the photoelectrons emitted have more energy.

15 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 141) Explanation of photoelectric effect by quantum theory 3. Photoelectric current directly proportional to intensity of radiation (b) By wave theory (cannot explain it) - if intensity of radiation increases, each electron would receive more energy and be emitted with greater speed

16 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 142) Explanation of photoelectric effect by quantum theory 4. Maximum kinetic energy of photoelectrons by Einstein’s photoelectron equation Maximum kinetic energy (KE max ) = hf – hf o (a) Einstein’s photoelectric equation - hf 0 = min. energy required for electron to escape from metal KE max = ½ mv 2 max = hf –  = hf – hf o

17 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 142) Explanation of photoelectric effect by quantum theory 4. Maximum kinetic energy of photoelectrons by Einstein’s photoelectron equation (b) Determination of KE max by I p -V graph photoelectron is only stopped from reaching anode when p.d. between cathode and anode is -V s (V s = stopping potential) KE max = eV s = hf – hf o

18 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 143) Explanation of photoelectric effect by quantum theory 4. Maximum kinetic energy of photoelectrons by Einstein’s photoelectron equation (c) Stopping potential - V s and KE max are increased with f - V s remains unchanged when intensity of radiation increases (intensity of light is related to no. of photons)

19 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 143) Explanation of photoelectric effect by quantum theory 4. Maximum kinetic energy of photoelectrons by Einstein’s photoelectron equation Note: Hence, KE max is independent of the intensity of radiation. (i) f = 0, KE max = -  = -hf 0 - determine  from intercept of KE max -axis

20 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 143) Explanation of photoelectric effect by quantum theory (ii) KE max = 0, f = f 0 Gradient = h Go to Example 2 Example 2 Go to Example 3 Example 3

21 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 146) Types of photocells 1. Photoemissive cell - consists of curved metal cathode and anode in vacuum tube - I p increases with intensity of radiation illuminated on cathode

22 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 146) Types of photocells 2. Photoconductive cell (light-dependent resistor) Resistance decreases when intensity of radiation illuminated increases - as potential divider light intensity , V’  light intensity , V’ 

23 © Manhattan Press (H.K.) Ltd Photoelectric effect (SB p. 146) Types of photocells Uses of photocells 1. Burglar alarm 2. Reproduction of sound from films

24 © Manhattan Press (H.K.) Ltd. End

25 © Manhattan Press (H.K.) Ltd. Electrons in photoelectric effect The ejected electrons in photoelectric effect possess kinetic energy while the ejected electrons in thermionic emission just “boil out”. Return to Text 23.2 Photoelectric effect (SB p. 136)

26 © Manhattan Press (H.K.) Ltd. When light falls on a metal surface, the energy of one photon can only be absorbed by one electron of a metal atom. Return to Text 23.2 Photoelectric effect (SB p. 140)

27 © Manhattan Press (H.K.) Ltd. Q: Q: A photocell is connected in the circuit as shown in Fig. (a). The cathode is illuminated with monochromatic radiation of wavelength 390 nm and the current I in the circuit is measured for different values of the applied potential difference V between the anode and cathode. The graph in Fig. (b) shows the results obtained. (a) Find the maximum kinetic energy of the photoelectrons. (b) What is the work function of the cathode? Give your answer in eV. (c) If the experiment is repeated using monochromatic radiation of wavelength 310 nm, where would the new graph cut the V-axis? Solution Fig. (a) Fig. (b) 23.2 Photoelectric effect (SB p. 144)

28 © Manhattan Press (H.K.) Ltd. Solution: (a) From the graph in Fig. (b), the reverse potential difference required to stop the photoelectrons from reaching the anode is –1.0 V. Hence, the maximum kinetic energy of the photoelectron = eV = e x 10 = 1.0 eV (b) From Einstein’s photoelectric equation, Maximum kinetic energy (KE max ) = hf – Φ ∴ Work function of cathode (Φ) = hf – KE max (c) If ’ = 310 nm, Maximum kinetic energy (KE max ) Hence, the graph would cut the V-axis at –1.8 V. Return to Text 23.2 Photoelectric effect (SB p. 144)

29 © Manhattan Press (H.K.) Ltd. Q: Q: Light photons of energy 3.4 eV each are incident on a plane cathode of work function 2.4 eV. Parallel and close to the cathode is a plane anode. Both the cathode and anode are inside an evacuated tube. (a) Find the maximum kinetic energy, in eV, of the photoelectrons emitted from the cathode. (b) Find the minimum value of the potential difference which should be applied between the cathode and anode in (i) normal to the cathode, and (ii) at an angle of 30° to the cathode. Solution 23.2 Photoelectric effect (SB p. 145)

30 © Manhattan Press (H.K.) Ltd. Solution: (a) From Einstein’s photoelectric equation, KE max = hf – Φ = 3.4 – 2.4 = 1.0 eV (b) (i) If V s = stopping potential, KE max = eV s,1.0 = eV s ∴ Stopping potential (V s )= 1.0 V with the anode negative with respect to the cathode. (ii) If the electrons are emitted at an angle of 30 o to the cathode, component of velocity along the direction of the stopping potential V s ’ is v sin30 o. Hence½ m (v sin30 o ) 2 = e V s ’ ½ mv 2 sin 2 30 o = e V s ’ (1.0) sin 2 30 o = e V s ’ ∴ V s ’ = 1.0 ×sin 2 30 o = 0.25 V Return to Text 23.2 Photoelectric effect (SB p. 145)