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Photoelectric effect & quantum behavior of light
1. PHOTOELECTRIC EFFECT & QUANTUM BEHAVIOR OF LIGHT
BY
GOUTAM SIR
P.G. DIPLOMA IN ASTRONOMY & PLANETARY SCIENCE & M.SC PHYSICS
2. PHOTOELECTRIC EFFECT & PHOTOELECTRON & PHOTOELECTRIC CURRENT
Photoelectric Effect: Heinrich Rudolf Hertz first observed
that when Electromagnetic radiation (of sufficiently high
frequency) strike onto the clean metal surface, electrons
started to emitted from the surface of the metal & This
Phenomena is called Photoelectric Effect.
Photoelectrons & Photoelectric Current: The electrons
emitted when electromagnetic radiation falls on surface
of certain materials are called photoelectrons.
Flow of photoelectrons is called photoelectric current.
The alkali metals, like lithium, sodium, potassium etc. emit photoelectrons, when
exposed to visible light. Ultraviolet radiations ejects electrons from zinc, magnesium
etc. using infrared rays, photoelectrons can be ejected from cesium.
3. THE HERTZ EXPERIMENTAL SET UP USED FOR STUDYING
THE PHOTOELECTRIC EFFECT
Setup: The set up consist of an evacuated glass
tube that has a photosensitive metal plate C and
another metal plate A as shown.
A monochromatic light source emerging from
the source (of sufficiently frequency) enters the
Quartz window and fall on photosensitive plate C,
is called emitter & it is given negative charge.
Working: When electromagnetic wave (light) fall
on photosensitive metal plate C which is called emitter. The plate C emits photoelectrons
due to photoelectric effect. The photo electrons emitted by plate C will be attracted
towards the positive plate A. these electron flows in the eternal circuit to cause an electric
current in the circuit. Such a current is known as the photoelectric current and measured
by the micrometer connected in the circuit.
Note: Additional voltage applied to the plates controls electron transport
4. EXPERIMENTAL RESULT OF PHOTOELECTRIC EFFECT
Effect of Intensity of Incident Light: i) The number of
photoelectrons i.e., photoelectric current can be increased
by increasing the intensity of light.
Effect of Potential on Photoelectric Current: At large
values of V i.e., potential of plate A, the current reaches a
maximum value. All the electrons emitted at C are collected at A
The maximum current increases as the intensity of the incident
light increases
When V is negative & less, the current drops
When V is equal to or more negative than Vs, the current
is zero & Vs & is called stopping potential.
This potential is independent of the intensity of the light,
as can be seen.
5. EXPERIMENTAL RESULT OF PHOTOELECTRIC EFFECT
Dependence of photoelectron kinetic energy on light intensity
Experimental Result: The maximum kinetic energy is
independent of light intensity.
Let
1
2
𝑚𝑣𝑚𝑎𝑥
2
be the maximum K.E of the electrons
stopped under the stopping potential 𝑉
𝑠.
Then
𝟏
𝟐
𝒎𝒗𝒎𝒂𝒙
𝟐
= 𝒆𝑽𝒔 ⇒ 𝒗𝒎𝒂𝒙 =
𝟐𝒆𝑽𝒔
𝒎
Effect of Frequency: i) K.E of the electron depends upon
frequency of the incident ray
Hence, Stopping potential depends upon frequency as well.
No electrons are emitted if the incident light falls below
some cutoff or thershold frequency,
The cutoff frequency is characteristic of the material being illuminated
6. SUMMARIZATION
Law of Photoelectric Emission: The result of experiments on photoelectric emission can
be formulated in the form of the following laws known as laws of photoelectric emission-
i) For a given photosensitive material, there is a minimum frequency below which there
is no photoelectric emission. This frequency is independent of the intensity of the light
& is called the threshold frequency.
ii) Photoelectric emission is an instantaneous phenomenon. There is no time lag
between the incidence of radiation & the emission of photoelectrons.
iii) The number of photoelectrons & the photoelectric current is directly proportional to
the intensity of incident radiation, provided the frequency 𝛎 is greater than the
threshold frequency.
iv) The kinetic energy of photoelectrons increases with the frequency of the incident
radiation & is independent of the intensity of radiation.
7. FAILURE OF WAVE THEORY OF LIGHT TO EXPLAIN PHOTOELECTRIC EFFECTS
The photoelectric effect could not be explained using wave theory. If we try to explain
we get all contradictory results, & these results are as follows:
According to wave theory when radiation strike the metal surface, photoelectrons will be
emitted from the surface of a metal only after about 200 days. However, experimentally
it is seen that ejection of electrons is instantaneous process.
According to wave theory, radiation of any strong frequency should eject electrons from
the metal, but experimentally it is seen that there is no ejection of electrons when the
frequency is less than the minimal frequency called threshold frequency.
According to wave theory the intensity of radiation depends upon the amplitude of the
wave & not on the frequency of the wave. So, if frequency of the wave is increased there
should not be increase in the velocity or kinetic energy of the electrons. However,
experimentally it is seen that if the frequency of incident radiation is increased there
was an increase in kinetic energy.
Thus, wave theory miserably failed to explain photoelectric effect. As it is seen that
wave theory of light failed to explain the photoelectric effects, so we need new kind of
theory to explain that.
8. THEORY THAT REDEFINE THE PHYSICS OF LIGHT
Planck’s Quantum Theory of Light: In 1900, Planck enunciated a new theory according
to which the electromagnetic radiation (light) is not continuous rather light is made of
tiny packet of energy called quantum or quanta
“The electromagnetic radiation is emitted or absorbed not continuously but
intermittently in integral multiple of a packets (atom) of energy called quantum or
quanta (atomicity of energy).”
The size & energy of quantum depends on the frequency of radiation. An oscillator
(source) can emit one quantum, two, three etc. The energy contained in one quantum
is
𝑬 = 𝒉𝝂
Where 𝜈 is the frequency of radiation & h is the Planck’s constant.
In S.I ℎ = 6.626 × 10−34
𝐽𝑠/4.14 × 10−15
𝑒𝑉𝑠
Energy of other quanta is integral multiple of energy of smallest quantum.
9. THEORY THAT REDEFINE THE PHYSICS OF LIGHT
Einstein’s Quantum Theory of Light: According to Einstein electromagnetic radiation is
consists (made) of small energetic particles (particle of energy) is called photons &
those energetics particles are not only emitted & absorbed but also it propagates
through space in with speed of light.
Energy of the photon is directly proportional to its frequency
Energy contain in each photon is given as
𝑬 = 𝒉𝝂
Where ℎ = 𝑃𝑙𝑎𝑛𝑐𝑘′
𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 & 𝜈 = Frequency of the photon.
10. CHARACTERISTICS OF PHOTONS
i) According to quantum theory, radiations are emitted or absorbed discontinuously in indivisible discrete packets of energy.
These packets are called quanta.
ii) Einstein called the quanta of energy consists of photons. Thus, radiation consists of particles called photons. & photons does
not contain matter but it is simple possesses energy.
iii) Einstein said that radiations are not only emitted or absorbed as photons, but also it is propagated through space in definite
quanta with velocity 3 × 108
𝑚𝑠−1
.
iv) Intensity of radiation depends on the number of photons crossing unit area per second. The intensity of radiation is given by
𝑰 = 𝑵𝒉𝝂Where 𝑁 is the number of photons crossing per unit area per seconds. But according to wave theory the intensity of
wave depends upon the square of the amplitude of the wave.
v) Photons will have its individuality until it falls on the atom. When the photons are absorbed by an atom, its identity is lost.
vi) Photons have zero rest mass & so photons cannot exist at rest. The mass of particle of mass 𝑚𝑂 (i.e., rest mass of particles)
moving with velocity 𝑣 is given by
𝑚 =
𝑚𝑂
1−
𝑣2
𝑐2
𝑤ℎ𝑒𝑟𝑒 𝑐 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡
∴ 𝑚𝑂 = 𝑚 1 −
𝑣2
𝑐2
𝑜𝑟
𝑚𝑂
𝑚
= 1 −
𝑣2
𝑐2
= 0
∴ 𝑖𝑓 𝑚𝑂 = 0 𝑡ℎ𝑒𝑛 𝑣 = 𝑐i.e., when the rest mass of the particle is zero, the particle moving with velocity of light viz. photons
particles.
vii) Photons do not have any charge, so they are not deflected in electric & magnetic fields. viii) Wavelength of photon change
from one medium to another so the velocity of photon is different in different media.
11. EXPLANATION OF PHOTOELECTRIC EFFECT USING QUANTUM THEORY OF
LIGHT
Let ℎ𝜈 = the energy of the incident photon on a photosensitive material where ℎ = the Planck’s constant & 𝜈 = is the frequency of the radiation, 𝑚 = mass of
electron, 𝑣 = velocity of emitted electrons & 𝑊 = The work function of the metal
Note: In the photoelectric process one photon is completely absorbed by one electron
When ℎ𝜈 energy completely given to one free electrons, part of it is used to extract the free electron to the surface of the material & the remaining is used to
impart K.E to emitted electron from the surface of the materials. ∴
1
2
𝑚𝑣2
= 𝑇ℎ𝑒 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝐾𝐸 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑚𝑖𝑡𝑡𝑒𝑑 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛, 𝑡ℎ𝑒𝑛,
𝒉𝝂 = 𝑾 +
𝟏
𝟐
𝒎𝒗𝟐 … 𝑖
This relation is known as Einstein’s Photoelectric Equation. Let 𝜈𝑂 = the threshold frequency required just to eject an electron to the surface, with zero kinetic
energy. Then, ℎ𝜈𝑂 = 𝑊
𝒉𝝂 = 𝒉𝝂𝑶 +
𝟏
𝟐
𝒎𝒗𝟐
… (𝒊𝒊)
𝒐𝒓 𝒉 𝝂 − 𝝂𝑶 =
𝟏
𝟐
𝒎𝒗𝟐 … (𝒊𝒊𝒊)
This equation shows that i) There is no photoelectric emission if 𝜈 < 𝜈𝑂 ii) The KE of the electrons increases with increase in the incident frequency ν. iii) If
frequency is kept constant & the intensity of light is increased, then more photons are incident on the metal surface each photon having the same energy.
Hence more electron are ejected are ejected, as an electron can absorb only one photon, each electron will have same maximum energy & will be ejected with
same maximum velocity. Hence, an increase in the intensity of incident light only increases the number of photoelectrons ejected & not their velocity. iv) The
stopping potential 𝑉
𝑠 is given by
𝒆𝑽𝒔 = 𝒉𝝂 − 𝒉𝝂𝑶As ℎ𝜈𝑂 is constant the stopping potential is proportional to the frequency of the incident photon. 𝑉
𝑠 is independent of intensity.
