UNIT 24 : QUANTIZATION OF LIGHT

1
UNIT 24 QUANTIZATION OF LIGHT
3 hours
24.1 Plancks Quantum Theory 24.2 The
Photoelectric Effect
2
SUBTOPIC
24 .1 Plancks Quantum Theory ½ hour
LEARNING OUTCOMES
At the end of this lesson, the students should
be able to

• Distinguish between Plancks quantum
• theory and classical theory of energy.
• b) Use Einsteins formulae for
• a photon energy, .

3
24.1 Plancks Quantum Theory

• The foundation of the Plancks 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.

Figure 1 Black Body Spectrum
5

• Rayleigh-Jeans and Wiens 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 Plancks 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
Comparison between Planck quantum theory and
classical theory of energy.
Plancks 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)
8

• According to this assumptions, the quantum E of
  the energy for radiation of frequency f is given
  by

where
Plancks 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 10-34 J s
1 eV1.60 x 10-19 J, me 9.11 x 10-31 kg, e
1.60 x 10-19 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 10-34 J s
1 eV1.60 x 10-19 J, me 9.11 x 10-31 kg, e
1.60 x 10-19 C)
13
SUBTOPIC
24 .2 The Photoelectric Effect 2 ½
hours
LEARNING OUTCOMES
At the end of this lesson, the students should
be able to

1. Explain the phenomenon of photoelectric effect.
2. Define and determine threshold frequency, work
   function and stopping potential.
3. Describe and sketch diagram of the photoelectric
   effect experimental set-up.
4. Explain the failure of wave theory to justify the
   photoelectric effect.

14
SUBTOPIC
24 .2 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 Einsteins
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).

16
9.2 The photoelectric effect

• The photoelectric effect can be measured using a
• device like that pictured in figure below.

A
The photoelectric effects experiment
17
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
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
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 effects experiment
B (After)
A (Before reversing the terminal)
20
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)
e.m. radiation (incoming light)
Anode(collector)
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
Einsteins theory of Photoelectric Effect

• According to Einsteins 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
Einsteins theory of Photoelectric Effect

• If the frequency f of the incoming light is so
  low
• that is hf lt Wo , then the photon will not
  have
• enough energy to eject any electron at all.
• If hf gt 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 Einsteins photoelectric
• equation ,

but
24
Einsteins theory of Photoelectric Effect
Einsteins photoelectric equation
photon energy
f frequency of em radiation /incoming light
maximum kinetic energy of ejected electron.
vmax maximum speed of the photoelectron
25
Einsteins 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
Einsteins theory of Photoelectric Effect
Electron is ejected.
Electron is emitted
hf gt Wo
hf
W0
Metal
hf lt 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 10-34 J s
1 eV1.60 x 10-19 J, me 9.11 x 10-31 kg, e
1.60 x 10-19 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 10-34 J s
1 eV1.60 x 10-19 J, me 9.11 x 10-31 kg, e
1.60 x 10-19 C)
K.Emax E Wo
29
Example 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 10-34 J s
1 eV1.60 x 10-19 J, me 9.11 x 10-31 kg, e
1.60 x 10-19 C)
Solution 24.5
a.
30
Solution 24.5
(Given c 3.00 x 108 m s-1, h 6.63 x 10-34 J s
1 eV1.60 x 10-19 J, me 9.11 x 10-31 kg, e
1.60 x 10-19 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 -1.70 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 10-34 J s , 1 eV1.60 x 10-19
  J,
• me 9.11 x 10-31 kg, e 1.60 x 10-19 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
10-34 J s , 1 eV1.60 x 10-19 J, mass of
electron m 9.11 x 10-31 kg, e 1.60 x 10-19
C)
34
Solution 24.7
Ans. 553 nm, 1.84 x 10-19 J
35
Graphs in Photoelectric Effect

• Generally, Einsteins photoelectric equation
  

K.Emax

f ? K.Emax ?
f
0
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.
W02 gt W01
f02 gt 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.
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.
Vs2 gt 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.
W02 gt W01
Vs1 gt Vs2
42
Example 24.8
K.Emax (x 10-19 J)

f(x 1014 )Hz
0
Use the graph above to find the value of i)
work function and ii) the threshold
wavelength.
43
Solution 24.8
44
OBSERVATIONS of the photoelectric effects
experiment

1. Electrons are emitted immediately
2. Stopping potential does not depend on the
   intensity of light.
3. Threshold frequency of light is different for
   different target metal.
4. 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 Einsteins 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
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
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 photons 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
4. ENERGY OF LIGHT
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 Plancks quantum theory which is Ehf Energy of light depends on its frequency.
49

• Experimental observations deviate from classical
  predictions based on Maxwells e.m. theory. Hence
  the classical physics cannot explain the
  phenomenon of photoelectric effect.
• The modern theory based on Einsteins 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
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 Depends on the light intensity. Depends only on the light frequency .
51
Exercise
(Given c 3.00 x 108 m s-1, h 6.63 x 10-34 J s
1 eV1.60 x 10-19 J, me 9.11 x 10-31 kg, e
1.60 x 10-19 C)
1. Find the energy of the photons in a beam
whose wavelength is 500 nm. ( 3.98 x 10 -19
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 0.063 V. When light of
  wavelength 440 nm is used, the stopping potential
  becomes 0.865 V. Determine the ratio
• ( 6.35 x 10-15 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 10-34 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
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.
(1.60 x 10-19 J, 3.85 x 10-19 J, -1.57 V)