1. UNIT 24 : QUANTIZATION OF LIGHT
3 hours
24.1 Planck’s Quantum Theory
24.2 The Photoelectric Effect

2. 24 .1 Planck’s Quantum Theory ½ hour
SUBTOPIC :
Planck’s Quantum Theory
½ hour
LEARNING OUTCOMES :
At the end of this lesson, the students should
be able to :
Distinguish between Planck’s quantum
theory and classical theory of energy.
b) Use Einstein’s formulae for
a photon energy,

3. 24.1 Planck’s Quantum Theory
The foundation of the Planck’s quantum theory is a
theory of black body radiation.
Black body is defined as an ideal system or object
that absorbs and emits all the em radiations that is
incident on it.
The electromagnetic radiation emitted
by the black body is called black body
radiation.
In an ideal black body, incident light is
completely absorbed.
Light that enters the cavity through the
small hole is reflected multiple times
from the interior walls until it is
completely absorbed.
black body

4. The spectrum of electromagnetic radiation emitted by the black body (experimental result) is shown in figure 1.
Experimental result
Rayleigh -Jeans theory
Wien’s theory
Classical physics
Figure 1 : Black Body Spectrum

5. Rayleigh-Jeans and Wien’s theories (classical
physics) failed to explain the shape of the black
body spectrum or the spectrum of light emitted by
hot objects.
Classical physics predicts a black body radiation
curve that rises without limit as the f increases.
The classical ideas are :
Energy of the e.m. radiation does not depend on its frequency or wavelength.
Energy of the e.m. radiation is continuously.

6. In 1900, Max Planck proposed his theory that is
fit with the experimental curve in figure 1 at all wavelengths known as Planck’s quantum theory.
The assumptions made by Planck in his theory are :
The e.m. radiation emitted by the black body
is a discrete (separate) packets of energy
known as quanta. This means the energy of
e.m. radiation is quantised.
The energy size of the radiation depends
on its frequency.

7. Planck’s Quantum Theory
Comparison between Planck’ quantum theory and classical theory of energy.
Planck’s Quantum Theory
Classical theory
Energy of the e.m radiation is quantised. (discrete)
Energy of the e.m radiation is continously.
Energy of e.m radiation depends on its frequency or wavelength
Energy of e.m radiation does not depend on its frequency or wavelength (depends on Intensity)
Photon

8. According to this assumptions, the quantum E of the energy for radiation of frequency f is given by
where
Planck’s quantum theory

9. Photons In 1905, Albert Einstein proposed that light comes in
bundle of energy (light is transmitted as tiny
particles), called photons.
Photon is defined as a particle with zero mass
consisting of a quantum of electromagnetic
radiation where its energy is concentrated.
Quantum means “fixed amount”

10. In equation form, photon energy (energy of photon)is
Unit of photon energy is J or eV.
The electronvolt (eV) is a unit of energy that can
be defined as the kinetic energy gained by an
electron in being accelerated by a potential
difference (voltage) of 1 volt.
Unit conversion :
Photons travel at the speed of light in a vacuum.
Photons are required to explain the photoelectric
effect and other phenomena that require light to
have particle property.

11. Example 24.1 Calculate the energy of a photon of blue light, .
(Given c = 3.00 x 108 m s-1, h = 6.63 x J s
1 eV=1.60 x J, me = 9.11 x kg, e = 1.60 x C)

12. Example 24.2
A photon have an energy of 3.2 eV. Calculate the frequency, vacuum wavelength and energy in joule of the photon.
(7.72 x 1014 Hz ,389 nm, 5.12 x10-19 J)
(Given c = 3.00 x 108 m s-1, h = 6.63 x J s
1 eV=1.60 x J, me = 9.11 x kg, e = 1.60 x C)

13. 24 .2 The Photoelectric Effect 2 ½ hours
SUBTOPIC :
The Photoelectric Effect
2 ½ hours
LEARNING OUTCOMES :
At the end of this lesson, the students should
be able to :
Explain the phenomenon of photoelectric effect.
Define and determine threshold frequency, work function and stopping potential.
Describe and sketch diagram of the photoelectric effect experimental set-up.
Explain the failure of wave theory to justify the photoelectric effect.

14. 24 .2 The Photoelectric Effect 2 ½ hours
SUBTOPIC :
The Photoelectric Effect
2 ½ hours
LEARNING OUTCOMES :
At the end of this lesson, the students should be able to :
e) Explain by using graph and equations the observations of photoelectric effect experiment in terms of the dependence of :
i ) kinetic energy of photoelectron on the frequency
of light;
½ mvmax2 = eVs = hf – hfo
ii ) photoelectric current on intensity of incident light;
iii) work function and threshold frequency on the
types of metal surface; Wo =hfo
f) Use Einstein’s photoelectric effect equation,
Kmax = eVs = hf – Wo

15. 24 .2 The photoelectric effect
The photoelectric effect is the emission of electrons
from the metal surface when electromagnetic
radiation of enough frequency falls/strikes/
incidents /shines on it.
A photoelectron is an electron ejected due to
photoelectric effect (an electron emitted from
the surface of the metal when light strikes its surface). -
em radiation
(light)
photoelectron
Metal surface
Free electrons

16. The photoelectric effect can be measured using a
device like that pictured in figure below.
Anode(collector)
Cathode (emitter or target metal)
photoelectron
glass -
rheostat
power supply
e.m. radiation (incoming light)
vacuum A V A
The photoelectric effect’s experiment

17. A negative electrode (cathode or target metal or
9.2 The photoelectric effect
A negative electrode (cathode or target metal or
emitter) and a positive electrode (anode or
collector) are placed inside an evacuated glass
tube.
The monochromatic light (UV- incoming light) of
known frequency is incident on the target metal.
The incoming light ejects photoelectrons from a
target metal.
The photoelectrons are then attracted to the
collector.
The result is a photoelectric current flows in
the circuit that can be measured with an ammeter.

18. When the positive voltage (potential difference)
9.1 The photoelectric effect
When the positive voltage (potential difference)
is increased, more photoelectrons reach the
collector , hence the photoelectric current also
increases.
As positive voltage becomes sufficiently large, the
photoelectric current reaches a maximum
constant value Im, called saturation current.
Saturation current is defined as the maximum constant value of photocurrent in which when all the photoelectrons have reached the anode.

19. If the positive voltage is gradually decreased, the
9.2 The photoelectric effect
If the positive voltage is gradually decreased, the
photoelectric current I also decreases slowly.
Even at zero voltage there are still some
photoelectrons with sufficient energy reach the
collector and the photoelectric current flows is Io .
Graph of photoelectric current against voltage for photoeclectric effect’s experiment
B (After)
A (Before reversing the terminal)

20. When the voltage is made negative by reversing
9.2 The photoelectric effect
When the voltage is made negative by reversing
the power supply terminal as shown in figure
below, the photoelectric current decreases since
most photoelectrons are repelled by the collector
which is now negative electric potential.
Cathode (emitter or target metal)
vacuum A V
e.m. radiation (incoming light)
Anode(collector) -
photoelectron
glass
Reversing power supply terminal
(to determine the stopping potential)
power supply
rheostat B

21. If this reverse voltage is small enough, the fastest
electrons will still reach the collector and there will
be the photoelectric current in the circuit.
If the reverse voltage is increased, a point is
reached where the photoelectric current reaches
zero – no photoelectrons have sufficient kinetic
energy to reach the collector.
This reverse voltage is called the stopping
potential , Vs.
Vs is defined as the minimum reverse potential (voltage) needed for electrons from reaching the collector.
By using conservation of energy :
(loss of KE of photoelectron = gain in PE) ;
K.Emax = eVs

22. Einstein’s theory of Photoelectric Effect
According to Einstein’s theory, an electron is
ejected/emitted from the target metal by a
collision with a single photon.
In this process, all the photon energy is
transferred to the electron on the surface of metal
target.
Since electrons are held in the metal by attractive
forces, some minimum energy,Wo (work function,
which is on the order of a few electron volts for
most metal) is required just enough to get an
electron out through the surface.

23. If the frequency f of the incoming light is so low
Einstein’s theory of Photoelectric Effect
If the frequency f of the incoming light is so low
that is hf < Wo , then the photon will not have
enough energy to eject any electron at all.
If hf > Wo , then electron will be ejected and
energy will be conserved (the excess energy
appears as kinetic energy of the ejected electron).
This is summed up by Einstein’s photoelectric
equation ,
but

24. f = frequency of em radiation /incoming light
Einstein’s theory of Photoelectric Effect
Einstein’s photoelectric equation
= photon energy
f = frequency of em radiation /incoming light
= maximum kinetic energy of
ejected electron.
vmax = maximum speed of the photoelectron

25. Wo = the work function of a metal.
Einstein’s theory of Photoelectric Effect
Wo = the work function of a metal.
= the minimum energy required (needed) to
eject an electron from the surface of
target metal. fo
= threshold frequency.
= minimum frequency of e.m. radiation
required to eject an electron from the
surface of the metal.
= threshold wavelength.
= maximum wavelength of e.m. radiation
required to eject an electron from the
surface of the target metal.

26. hf > Wo hf < Wo vmax hf hf - v=0 - W0 W0 Metal hf W0 - Metal
Einstein’s theory of Photoelectric Effect - hf
v=0
Metal W0 - hf
vmax
Metal W0
Electron is ejected.
Electron is emitted
hf > Wo hf W0
Metal -
hf < Wo
No electron is ejected.

27. Example 24 .3
The work function for a silver surface is Wo = 4.74 eV. Calculate the
minimum frequency that light must have to eject electrons from the surface.
maximum wavelength that light must have to eject electrons from the surface.
(Given c = 3.00 x 108 m s-1, h = 6.63 x J s
1 eV=1.60 x J, me = 9.11 x kg, e = 1.60 x C)

28. Example 24.4
What is the maximum kinetic energy of electrons ejected from calcium by 420 nm violet light, given the work function for calcium metal is 2.71 eV?
(Given c = 3.00 x 108 m s-1, h = 6.63 x J s
1 eV=1.60 x J, me = 9.11 x kg, e = 1.60 x C)
K.Emax = E – Wo

29. Example 24.5 Solution 24.5 Sodium has a work function of 2.30 eV.
Calculate
a. its threshold frequency,
b. the maximum speed of the photoelectrons
produced when the sodium is illuminated by
light of wavelength 500 nm,
c. the stopping potential with light of this
wavelength.
(Given c = 3.00 x 108 m s-1, h = 6.63 x J s
1 eV=1.60 x J, me = 9.11 x kg, e = 1.60 x C)
Solution 24.5 a.

30. Solution 24.5 b. c. (Given c = 3.00 x 108 m s-1, h = 6.63 x 10-34 J s
1 eV=1.60 x J, me = 9.11 x kg, e = 1.60 x C) b. c.

31. Example 24.6
In an experiment of photoelectric effect, no current flows through the circuit when the voltage across the anode and cathode is V. Calculate
a. the work function, and
b. the threshold wavelength of the metal (cathode) if it is illuminated by ultraviolet radiation of frequency 1.70 x 1015 Hz.
(Given : c = 3.00 x 108 m s-1,
h = 6.63 x J s , 1 eV=1.60 x J,
me = 9.11 x kg, e = 1.60 x C)

32. Solution 24.6

33. Example 24.7
The energy of a photon from an electromagnetic wave is 2.25 eV
a. Calculate its wavelength.
b. If this electromagnetic wave shines on a metal, photoelectrons are emitted with a maximum kinetic energy of 1.10 eV. Calculate the work function of this metal in joules.
(Given c = 3.00 x 108 m s-1, h = 6.63 x J s ,
1 eV=1.60 x J, mass of electron m = 9.11 x kg, e = 1.60 x C)

34. Solution 24.7
Ans. : 553 nm, 1.84 x J

35. Graphs in Photoelectric Effect
Generally, Einstein’s photoelectric equation;
K.Emax
f ↑ K.Emax ↑ f

36. Graphs in Photoelectric Effect
f ↑ Vs ↑

37. Graphs in Photoelectric Effect
Variation of stopping voltage Vs with frequency f of the radiation for different metals but the intensity is fixed.
W01
W02
W02 > W01
f02 > f01

38. Graphs in Photoelectric Effect
Variation of photoelectric current I with voltage V for the radiation of different intensities but its frequency and metal are fixed.
Intensity 2x
Intensity 1x Vs

39. Notes:
Classical physics
Light intensity ,
Quantum physics
Light intensity ,
Light intensity ↑ ,
number of photons ↑ ,
number of electrons ↑ ,
current ↑
(If light intensity ↑, photoelectric current ↑).

40. Graphs in Photoelectric Effect
Variation of photoelectric current I with voltage V for the radiation of different frequencies but its intensity and metal are fixed. f2 f1
f2 > f1
Vs2 > Vs1
f ↑ Vs ↑

41. Graphs in Photoelectric Effect
Variation of photoelectric current I with voltage V for the different metals but the intensity and frequency of the radiation are fixed.
W01
W02
W02 > W01
Vs1 > Vs2

42. Example 24.8 Use the graph above to find the value of
K.Emax (x J)
f(x 1014 )Hz
Use the graph above to find the value of
i) work function and
ii) the threshold wavelength.

43. Solution 24.8
K.Emax (x J)
f(x 1014 )Hz

44. of the photoelectric effects experiment
OBSERVATIONS
of the photoelectric effects experiment
Electrons are emitted immediately
Stopping potential does not depend on the intensity of light.
Threshold frequency of light is different for different target metal.
Number of electrons emitted of the photoelectron current depend on the intensity of light.

45. EXPLAIN the failure of classical theory to justify the
photoelectric effect.
1. MAXIMUM KINETIC ENERGY OF PHOTOELECTRON
Clasiccal prediction
Experimental Result
Modern Theory
The higher the intensity, the greater the energy imparted to the metal surface for emission of photoelectrons.
The higher the intensity of light the greater the kinetic energy maximum of photoelectrons.
Very low intensity but high frequency radiation could emit photoelectrons. The maximum kinetic energy of photoelectrons is independent of light intensity.
Based on Einstein’s photoelectric equation:
The maximum kinetic energy of photoelectron depends only on the light frequency .
The maximum kinetic energy of photoelectrons DOES NOT depend on light intensity.

46. Clasiccal prediction Experimental Result Modern Theory
2. EMISSION OF PHOTOELECTRON ( energy )
Clasiccal prediction
Experimental Result
Modern Theory
Emission of photoelectrons occur for all frequencies of light. Energy of light is independent of frequency.
Emission of photoelectrons occur only when frequency of the light exceeds the certain frequency which value is characteristic of the material being illuminated.
When the light frequency is greater than threshold frequency, a higher rate of photons striking the metal surface results in a higher rate of photoelectrons emitted. If it is less than threshold frequency no photoelectrons are emitted. Hence the emission of photoelectrons depend on the light frequency.

47. Clasiccal prediction Experimental Result Modern Theory
3. EMISSION OF PHOTOELECTRON ( time )
Clasiccal prediction
Experimental Result
Modern Theory
Light energy is spread over the wavefront, the amount of energy incident on any one electron is small. An electron must gather sufficient energy before emission, hence there is time interval between absorption of light energy and emission. Time interval increases if the light intensity is low.
Photoelectrons are emitted from the surface of the metal almost instantaneously after the surface is illuminated, even at very low light intensities.
The transfer of photon’s energy to an electron is instantaneous as its energy is absorbed in its entirely, much like a particle to particle collision. The emission of photoelectron is immediate and no time interval between absorption of light energy and emission.

48. Energy of light depends only on amplitude
Clasiccal prediction
Experimental Result
Modern Theory
Energy of light depends only on amplitude
( or intensity) and not on frequency.
Energy of light depends on frequency
According to Planck’s quantum theory which is
E=hf
Energy of light depends on its frequency.

49. Experimental observations deviate from classical predictions based on Maxwell’s e.m. theory. Hence the classical physics cannot explain the phenomenon of photoelectric effect.
The modern theory based on Einstein’s photon theory of light can explain the phenomenon of photoelectric effect.
It is because Einstein postulated that light is quantized and light is emitted, transmitted and reabsorbed as photons.

50. Electrons are emitted SUMMARY : Comparison between classical physics
and quantum physics about photoelectric effect experiment
Feature
Classical physics
Quantum physics
Threshold frequency
An incident light of any frequency can eject electrons (does not has threshold frequency), as long as the beam has sufficient intensity.
To eject an electron, the incident light must have a frequency greater than a certain minimum value, (threshold frequency) , no matter how intense the light.
Maximum kinetic energy
of photoelectrons
Depends on the light intensity.
Depends only on the light frequency .
Emission of photoelectrons
There should be some delays to emit electrons from a metal surface.
Electrons are emitted
spontaneously.
Energy of light

51. Exercise (Given c = 3.00 x 108 m s-1, h = 6.63 x 10-34 J s
1 eV=1.60 x J, me = 9.11 x kg, e = 1.60 x C)
1. Find the energy of the photons in a beam whose
wavelength is 500 nm. ( 3.98 x J)
2. Determine the vacuum wavelength corresponding to a -ray
energy of 1019 eV. (1.24 x10-25 m)
3. A sodium surface is illuminated with light of wavelength
300 nm. The work function for sodium metal is 2.46 eV. Calculate
a) the kinetic energy of the ejected photoelectrons
b) the cutoff wavelength for sodium
c) maximum speed of the photoelectrons.
(1.68 eV, 505 nm, 7.68 x 105 ms-1)

52. 4. Radiation of wavelength 600 nm is incidents upon the surface of a metal. Photoelectrons are emitted from the surface with maximum speed 4.0 x 105 ms-1. Determine the threshold wavelength of the radiation. (7.7 x 10-7 m)
Determine the maximum kinetic energy, in eV, of photoelectrons emitted from a surface which has a work function of 4.65 eV when electromagnetic radiation of wavelength 200 nm is incident on the surface. (1.57 eV)
6. When light of wavelength 540 nm is incident on the cathode of photocell, the stopping potential obtained is V. When light of wavelength 440 nm is used, the stopping potential becomes V. Determine the ratio
( 6.35 x J s C-1)

53. In an experiment on the photoelectric effect, the following data were collected.
a. Calculate the maximum velocity of the photoelectrons
when the wavelength of the incident radiation is 350 nm.
b. Determine the value of the Planck constant from the
above data.
Wavelength of e.m. radiation, (nm)
Stopping potential, Vs (V)
350
1.70
450
0.900
(7.73 x 105 m s-1, 6.72 x J s)

54. 8. In a photoelectric effect experiment it is observed that no current flows unless the wavelength is less than 570 nm. Calculate
a. the work function of this material in electronvolts.
b. the stopping voltage required if light of wavelength 400 nm is used.
(2.18 eV, 0.92 V)

55. 9. In a photoelectric experiments, a graph of the light frequency f is plotted against the maximum kinetic energy Kmax of the photoelectron as shown in figure below.
Based on the graph, for the light frequency of 6.00 x 1014 Hz, calculate
a. the threshold frequency.
b. the maximum kinetic energy of the photoelectron.
c. the maximum velocity of the photoelectron.

56. a. Calculate the maximum kinetic energy of the photoelectron.
10. A photocell with cathode and anode made of the same metal connected in a circuit as shown in the figure below. Monochromatic light of wavelength 365 nm shines on the cathode and the photocurrent I is measured for various values of voltage V across the cathode and anode. The result is shown in the graph.
a. Calculate the maximum kinetic energy of the photoelectron.
b. Deduce the work function of the cathode.
c. If the experiment is repeated with monochromatic light of
wavelength 313 nm, determine the new intercept with the
V-axis for the new graph.
365 nm V G
(1.60 x J, 3.85 x J, V)