Photoelectric Effect

Photoelectric Effect: Scientists have been trying to figure out the behaviour of light using its properties to categorize it as a wave or a particle. Light seems to behave as both a particle and wave. Properties like interference, dispersion, diffraction support the wave nature of the light whereas the phenomenon like photoelectric effect support quantization of light and particle nature of the light. We can say that light shows the dual nature of both wave and particle.

In this article, we will learn more about the photoelectric effect which was given by the famous scientist Albert Einstein which supports the particle nature of light.

What is Photoelectric Effect?

Photoelectric effect of light is a phenomenon in which metal emits electrons from its valence shell when illuminated with light. The emitted electron is known as photoelectron, and this phenomenon is commonly known as photoemission. This phenomenon could not be explained if we considered light to be a wave, but if we consider the light to be a particle, then we can explain this phenomenon.

Photoelectric effect was first observed by Wilhelm Ludwig Franz Hallwachs, and it was verified by Heinrich Rudolf Hertz. Einstein explained this phenomenon and the quantum nature of light. Einstein was also honoured with the Nobel prize in \(1921\) for his work on Photoelectric effect.

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Light, a Wave or Particle?

Scientists have been trying to categorize light as a wave or a particle, but the light wave shows or exhibits the properties of both the wave and particle.

Light shows the phenomenon of dispersion, diffraction, interference etc., which support the behaviour of light as a wave.

But light also shows the properties which could not be explained if we consider the light to be a wave and could only be explained if we consider it to be a particle.

Therefore, light cannot be categorized exclusively as a wave or a particle and thus, it is known to have dual nature of both wave and particle.

Principle of Photoelectric Effect

In photoelectric effect, a metal surface is illuminated with light, and when light falls on the surface of the metal, the photoemission takes place, and photoelectron are ejected from the surface of the metal.

The energy of the photon of the wave gets transferred to the electrons of the metal atom, due to which the electrons get excited and are ejected with some velocity.

Important Terms Related to Photoelectric Effect

Work function: It is the minimum energy required to bring out the electron from the valence shell of the metal. It depends on the metal we are using. Only for the frequencies which are greater than the threshold frequency, the photoelectric effect will occur, but if the frequency of the light wave is less than the threshold frequency, the photoelectric effect will not happen.

Threshold frequency: It is the minimum frequency of the photon which is just sufficient to bring out the photoelectrons or provide the energy equal to the work function of the metal. It depends on the metal we are using.

Stopping potential: It is the potential required to stop the electron with the maximum kinetic energy. It depends on the frequency of the incident light. it gives us the measure of the maximum kinetic energy of the photoelectron.

Photocurrent: The current which is generated due to the photoelectric effect is known as photocurrent. It depends on the intensity of the incident light.

Photon

Photon is the quanta of the light; that is, light is constituted by packets of quanta of energy known as Photon. Each photon contains a certain amount of energy and momentum.

Energy of the photon is given by,

\(E=hν\)

Where,

\(h\) is the plank’s constant. The value of plank constant is \(h = 6.626 \times {10^{ – 34}}{\rm{J}}\,{\rm{s}}\)

\(v\) is the frequency of the light.

Momentum of photon is given by,

\(p = \frac{h}{\lambda }\)

Where,

\(\lambda \) is the wavelength of the light.

\(h\) is the plank’s constant.

Equation of Photoelectric Effect

The energy of the photon is equal to the sum of the threshold energy of the metal and the kinetic energy of the photoelectron.

Thus, the equation of photoelectric wave is given by,

\(K{E_{\max }} = hv – \phi \)

Where,

\(K{E_{\max }}\) is the maximum kinetic energy of the photoelectron

\(hv\) is the energy of the photon.

\(\varphi \) is the work function of the metal

Work function is dependent on the metal we are taking into consideration and will change if we change the metal. Sometimes the work function is expressed in terms of threshold frequency i.e., frequency of the light for which the maximum kinetic energy of the emitted Photoelectron is zero.

\(\phi = h{v_0}\)

Where,

\({v_0}\) is the threshold frequency.

\(h\) is the plank’s constant.

It is important to note that on increasing the intensity of the light, the maximum kinetic energy remains the same, only the value of photocurrent increases.

Sample Problems

Q.1. Light of wavelength \(4000\,Å\) is incident on a metal plate whose work function is \(2\,\rm{eV}.\) What is the maximum kinetic energy of emitted photoelectron?
Ans: The wavelength of light is \(\lambda = 4000\,Å\) and work function, \({\varphi _0} = 2\,\rm{eV}\)
From the Einstein Photoelectric equation, the maximum kinetic energy of photoelectron is given by,
\({K_{\max }} = \left( {\frac{{hc}}{\lambda } – {\varphi _0}} \right)\)
where \(‘h’\) is Planck’s constant and \(‘c’\) is the speed of light in a vacuum.
\({K_{\max }} = \left( {\frac{{6.6 \times {{10}^{ – 34}} \times 3 \times {{10}^8}}}{{4000 \times {{10}^{ – 10}}}} – 2 \times 1.6 \times {{10}^{ – 19}}} \right)\)
\({K_{\max }} = \frac{{4.95 \times {{10}^{ – 19}}}}{{1.6 \times {{10}^{ – 19}}}}\,{\rm{eV}} – 2\,{\rm{eV}} = 1.1\,{\rm{eV}}\)
The maximum kinetic energy \(1.1\,\rm{eV}.\)

Q.2. The value of retarding potential needed to stop the photoelectrons ejected from a metal surface of work function \(1.2\,\rm{eV}\) with the light of energy \(2\,\rm{eV}\) is
Ans: Work function of the metal\(\varphi = 1.2\,{\rm{eV}}\) and energy of the photons is \(hν=2\,\rm{eV}.\)
From the Einstein photoelectric equation, the maximum kinetic energy of the photoelectrons is given by,
\(eV = hv – \varphi \)
Where \(‘V’\) is retarding potential or stopping potential.
\(h\) is the plank’s constant.
\(\varphi \) is the work function of the metal.
\(V = \frac{{2\,\rm{eV} – 12\,\rm{eV}}}{e} = 0.8\,\rm{V}\)
Thus, the retarding potential is \(0.8\,\rm{V}\)

Summary

In this article, we learnt about the phenomenon which is explained only by the particle nature of the light. We came to know the constituent particle that light is made up of is known as a photon. Photons are packets of energy that possess some momentum, but the rest mass of the photon is zero. We learnt that on increasing the intensity of the light, the maximum kinetic energy of the photoelectron remains the same, and only the value of the photocurrent increases. The maximum kinetic energy of the photoelectron for a particular metal only depends on the frequency of the incident light. Work function is the minimum work done required to emit a photoelectron from a metal. It depends on the metal. The threshold frequency is the frequency of the light just sufficient to emit photoelectron, i.e., the kinetic energy of the photoelectron is zero.

Frequestly Asked Questions on Photoelectric Effect

Q.1. Is light a wave or a particle?
Ans: Light is both wave and a particle, that is, it exhibits the properties of both the wave and the particle.
Properties like diffraction and interference can be explained if we consider the light to be the wave, whereas the properties like the photoelectric effect can only be explained if we consider light to be a particle.

Q.2. What is the mass of a photon?
Ans: The rest mass of the photon is zero that means if the photon is moving, then it will have some momentum which signifies mass, but at rest, the mass of the photon will be zero.

Q.3. Will the maximum kinetic energy increase if we increase the intensity of the incident light?
Ans: No, the maximum kinetic energy will not increase if we increase the intensity of the light. The maximum kinetic energy only depends on the frequency of the incident light. On increasing the intensity, the number of photoelectrons will increase, thereby increasing the photocurrent.

Q.4. What is threshold frequency?
Ans: The threshold frequency is the frequency of the light which is just sufficient to emit photoelectron and for which the kinetic energy of the photoelectron is zero. Energy associated with threshold frequency is equal to the work function of the metal.

Q.5. What is stopping potential?
Ans: Stopping potential is the minimum potential applied for which none of the photoelectrons reaches the anode when the illuminated metal is kept at the cathode.

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