Photoelectric effect -derivations

1. ENGINEERING PHYSICS
PHY1071

2. • Photo Electric Effect
• Numerical Examples
Module :2 Quantum Physics

3. PHOTO ELECTRIC EFFECT

4. PHOTO ELECTRIC EFFECT
•Describe physical characteristics of the photoelectric effect
•Explain why the photoelectric effect cannot be explained by classical physics
•Describe how Einstein’s idea of a particle of radiation explains the
photoelectric effect

6. • Definition
The phenomenon of emission of electrons from a metal surface when illuminated by light of suitable frequency is
called the photoelectric effect.
• Photoelectric effect was discovered by H. Hertz in 1887.
• Photoelectrons & Photoelectric current:
• The photoelectric effect involves conversion of light energy into electrical energy. The electrons emitted
during photoelectric effect are called photoelectrons and the current constituted by photoelectrons is
called the photoelectric current.
• Threshold Frequency:
• The minimum frequency of the incident radiation required for the emission of electrons from the surface
of a metal is called the threshold frequency of the metal.
• Threshold frequency varies from metal to metal. It has been observed that metals like zinc, cadmium,
magnesium etc. shows photoelectric effect only for ultraviolet light.
• But some alkali metals like lithium, sodium, potassium, caesium and rubidium shows photoelectric effect
even for visible light.

7. Experimental Set up
• The experimental set-up consists of an evacuated glass tube which contains two
electrodes, a cathode C and an anode A, which are sealed inside the tube .
• The tube contains a side window of quartz which allows light of reasonably short
wavelength to pass through and allows to falls on cathode C.
• The electrons emitted from cathode C will move towards the anode A.
• This will constitutes the photoelectrons and causes photoelectric current to flow
in the circuit and measured using a micro ammeter connected in the circuit.
• The photoelectric current can be increased or decreased by varying the
magnitude and sign of the anode potential with respect to the cathode.
• Cut off Potential:
• It is observed that there is a certain minimum negative (retarding) potential
at anode which will reduce the photoelectric current to be zero and is
referred as stopping potential or retarding potential or cut-off potential,
represented as Vs .
Defn: Therefore the stopping potential is defined as the minimum negative
potential required at the anode so as to completely suppress the
photoelectrons reaching the anode and hence the current to zero in the circuit.
Experimental setup for Photo Electric Effect
Photo current VS applied voltage for different
intensities of incident light
High Intensity
Low Intensity

8. Experimental Observations:
1. Photoelectric effect is an instantaneous process. Photoelectrons
will ejected out within 10–9s (very small time) after light
irradiation on the metal surface.
2. For a given photosensitive material, there exist a certain
minimum frequency called the cut-off or threshold frequency
below which no photoelectric effect takes place.
3. For a given photosensitive material and frequency of incident
radiation (more than threshold frequency) the photoelectric
current is directly proportional to the intensity of incident light.
4. Effect of potential at anode: The graph of photoelectric current
and the voltage applied between the electrodes (cathode C and
anode A) shows that initially the photoelectric current increases
with the increasing potential. For a certain potential, the current
becomes maximum. For further increase in potential, the graph
shows saturation of current (Horizontal portion).
5. The value of stopping potential increases with increase in
frequency of the incident radiation
6. The kinetic energy of the photoelectrons increases linearly with
the frequency of the incident radiations . It is independent of
the intensity of the incident radiations.
Photo current VS applied voltage for different
intensities of incident light
Photo current VS applied voltage for different
frequencies incident light

9. 1. The number of photoelectrons emitted per second from the
metal surface is directly proportional to the intensity of
incident light.
2. The maximum Kinetic Energy of emitted photoelectrons does
not depend upon the intensity of incident light.
3. The maximum Kinetic Energy of emitted photoelectrons
increases linearly with increase in frequency of incident light.
4. If the frequency of incident light is less than certain minimum
value, then no photoelectrons emitted from the metal surface
whatever may be the intensity of incident light. This minimum
frequency (threshold frequency) is different for different
metals.
5. Photoelectric process is instantaneous i.e., there is no time-lag
between incidence of light and emission of photoelectrons.
Classical physics failed to explain the observed laws on the basis
of electromagnetic theory.
Results obtained from Experimental Observations:

10. • Einstein used Plank’s Quantum Theory of light (light beam consists of photons).
• Work function. 𝜑 in eV (minimum energy required by the electron
to come out of the metal surface at a velocity ‘v’)
• When the photon of Energy E hits the metal,
𝐸 = ℎ𝑓
• The energy of the photon is released in two ways
1. The part of absorbed photon energy is used in releasing the electron
from the metal surface
2.The remaining energy appears as the kinetic energy of the electron.
𝐸𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑝ℎ𝑜𝑡𝑜𝑛 ′
𝐸′
= 𝐵𝑖𝑛𝑑𝑖𝑛𝑔 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 + 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛
ℎ𝑓 = 𝜑 +
1
2
𝑚𝑣𝑚𝑎𝑥
2
𝐾. 𝐸 =
1
2
𝑚𝑣𝑚𝑎𝑥
2 = ℎ𝑓 − 𝜑
• Work function is different for different metals. If f0 is the threshold frequency
then
𝜑 = ℎ𝑓0
𝐾. 𝐸 =
1
2
𝑚𝑣𝑚𝑎𝑥
2
= ℎ𝑓 − 𝜑 = ℎ𝑓 − ℎ𝑓0 = ℎ(𝑓 − 𝑓0)
Einstein’s Photoelectric Equation
Typical Values of the Work
Function for Some Common
Metals
Metal (eV)
Na 2.46
Al 4.08
Pb 4.14
Zn 4.31
Fe 4.50
Cu 4.70
Ag 4.73
Pt 6.35

11. Cut-off frequency (𝒇𝒄)
• Photoelectric effect follows from because the kinetic energy of the photoelectron can take only positive values.
This means that there must be some threshold frequency for which the kinetic energy is zero.
𝑲. 𝑬 =
𝟏
𝟐
𝒎𝒗𝒎𝒂𝒙
𝟐 = 𝒉𝑨 = 𝒇𝒄 − 𝝋 = 𝟎; =⇒ 𝒇𝒄 =
𝝋
𝒉
• Cut-off frequency depends only on the work function of the metal and is in direct proportion to it.
When the work function is large (when electrons are bound fast to the metal surface), the energy of the
threshold photon must be large to produce a photoelectron, and then the corresponding threshold frequency is large.
Because frequency f and wavelength of electromagnetic waves are related by the fundamental
relation 𝝀𝒄 =
𝒄
𝒇𝒄
=
𝒄
𝝋/𝒉
=
𝒉𝒄
𝝋
; where hc=1240eVnm
(where is the speed of light in vacuum), the cut-off frequency has its corresponding cut-off
wavelength
• When the incident radiation has wavelengths longer than the cut-off wavelength, the
photoelectric effect does not occur.
Cut-off wave length (𝒇𝒄)

12. 1. A sodium surface is illuminated with light having a wavelength of 300 nm. The work function for sodium metal is
2.46 eV. Find A. The maximum kinetic energy of the ejected photoelectrons and B. The cutoff wavelength for
sodium. Ans: 1.678 eV, 504.6 nm
2. Molybdenum has a work function of 4.2eV. (a) Find the cut off wavelength and cut off frequency for the
photoelectric effect. (b) What is the stopping potential if the incident light has wavelength of 180 nm? Ans: 295.5
nm, 1.015×1015 Hz, 2.696 V
3. Electrons are ejected from a metallic surface with speeds up to 4.60 x 105 m/s when light with a wavelength of
625 nm is used. (a) What is the work function of the surface? (b) What is the cut-off frequency for this surface?
Ans: 1.38 eV, 3.34×1014 Hz

13. 1. A sodium surface is illuminated with light having a wavelength of 300 nm. The work function for sodium metal is
2.46 eV. Find (A). The maximum kinetic energy of the ejected photoelectrons (B). The cutoff wavelength for
sodium. Ans: 1.678 eV, 504.6 nm

14. 1. A sodium surface is illuminated with light having a wavelength of 300 nm. The work function for sodium metal is
2.46 eV. Find (A). The maximum kinetic energy of the ejected photoelectrons (B). The cutoff wavelength for
sodium. Ans: 1.678 eV, 504.6 nm

15. 2. Molybdenum has a work function of 4.2eV. (a) Find the cut off wavelength and cut off frequency for the
photoelectric effect. (b) What is the stopping potential if the incident light has wavelength of 180 nm? Ans: 295.5
nm, 1.015×1015 Hz, 2.696 V

16. 2. Molybdenum has a work function of 4.2eV. (a) Find the cut off wavelength and cut off frequency for the
photoelectric effect. (b) What is the stopping potential if the incident light has wavelength of 180 nm? Ans: 295.5
nm, 1.015×1015 Hz, 2.696 V

17. 3. Electrons are ejected from a metallic surface with speeds up to 4.60 x 10^5 m/s when light with a wavelength of 625
nm is used. (a) What is the work function of the surface? (b) What is the cut-off frequency for this surface?
Ans: 1.38 eV, 3.34×1014 Hz

18. 3. Electrons are ejected from a metallic surface with speeds up to 4.60 x 10^5 m/s when light with a wavelength of 625
nm is used. (a) What is the work function of the surface? (b) What is the cut-off frequency for this surface?
Ans: 1.38 eV, 3.34×1014 Hz

19. Numericals
1. Photoelectric Effect for Silver Radiation with wavelength 300 nm is incident on a silver surface. Will photoelectrons be
observed?
2. Work Function and Cut-Off Frequency When a 180-nm light is used in an experiment with an unknown metal, the
measured photocurrent drops to zero at potential – 0.80 V. Determine the work function of the metal and its cut-off
frequency for the photoelectric effect.
3. The Photon Energy and Kinetic Energy of Photoelectrons A 430-nm violet light is incident on a calcium photoelectrode
with a work function of 2.71 eV. Find the energy of the incident photons and the maximum kinetic energy of ejected
electrons.
4. A yellow 589-nm light is incident on a surface whose work function is 1.20 eV. What is the stopping potential? What is
the cut-off wavelength?

20. 1. For the same monochromatic light source, would the photoelectric effect occur for all metals?
2. In the interpretation of the photoelectric effect, how is it known that an electron does not absorb more
than one photon?
3. Explain how you can determine the work function from a plot of the stopping potential versus the
frequency of the incident radiation in a photoelectric effect experiment. Can you determine the value of
Planck’s constant from this plot (Ans from the slope)
4. Suppose that in the photoelectric-effect experiment we make a plot of the detected current versus the
applied potential difference. What information do we obtain from such a plot? Can we determine from
it the value of Planck’s constant? Can we determine the work function of the metal?
5. Speculate how increasing the temperature of a photoelectrode affects the outcomes of the photoelectric
effect experiment.
6. Which aspects of the photoelectric effect cannot be explained by classical physics?
7. Is the photoelectric effect a consequence of the wave character of radiation or is it a consequence of the
particle character of radiation? Explain briefly the particle character
8. The metals sodium, iron, and molybdenum have work functions 2.5 eV, 3.9 eV, and 4.2 eV, respectively.
Which of these metals will emit photoelectrons when illuminated with 400 nm light?
Conceptual Questions

21. Summary
 The photoelectric effect occurs when photoelectrons are ejected from a metal surface
in response to monochromatic radiation incident on the surface. It has three
characteristics: (1) it is instantaneous, (2) it occurs only when the radiation is above a
cut-off frequency, and (3) kinetic energies of photoelectrons at the surface do not
depend of the intensity of radiation. The photoelectric effect cannot be explained by
classical theory.
 We can explain the photoelectric effect by assuming that radiation consists of photons
(particles of light). Each photon carries a quantum of energy. The energy of a photon
depends only on its frequency, which is the frequency of the radiation. At the surface,
the entire energy of a photon is transferred to one photoelectron.
 The maximum kinetic energy of a photoelectron at the metal surface is the difference
between the energy of the incident photon and the work function of the metal. The
work function is the binding energy of electrons to the metal surface. Each metal has
its own characteristic work function.