Photoelectric Effect | Einstein’s Equation

Photoelectric Effect-

 

It is a phenomenon of emission of electrons from metal surfaces exposed to light energy of suitable frequency.

 

  • The electrons emitted by the metal surface are called as photoelectrons.
  • The electric current constituted by photoelectrons is called as photoelectric current.

 

 

Concept-

 

  • Consider a metal piece having free electrons.
  • Suppose an electron leaves the metal piece at the cost of its own energy.
  • This makes the metal piece positively charged.
  • The electrostatic force of attraction starts acting between the positive charge and the electron.
  • This force tries to stop the electron to escape out the electric field of the positive charge.
  • To escape out, electron must posses certain amount of energy.

 

Now, we define the following terms-

 

Threshold Energy-

 

  • It is the minimum amount of energy required to liberate the electrons from the metal surface.
  • It is also called as work function.
  • Work function is different for different metals.
  • Its unit is Joule or eV (electron volt).
  • For a metal, low work function is desirable.

 

Threshold Frequency-

 

It is the minimum frequency that the light must possess to liberate the electrons from the metal surface.

 

Threshold Wavelength-

 

It is the maximum wavelength that the light can possess to liberate the electrons from the metal surface.

 

Expression for Threshold Wavelength-

 

Let-

  • W0 = Work function
  • h = Planck’s constant = 6.6 x 10-34 Joule-sec
  • ν0 = Threshold frequency
  • λ0 = Threshold wavelength
  • c = speed of light = 3 x 108 m/sec

 

Then, we have-

 

 

This is the required expression for threshold wavelength.

 

Einstein’s Photoelectric Equation-

 

Consider-

  • A photon of energy hν falls on a metal surface.
  • The energy of this photon is absorbed by a free electron in the metal.

 

According to Einstein, this absorbed energy hν is utilized for two purposes-

 

Purpose-01:

 

  • A part of energy is used by the electron to overcome the surface barrier.
  • This part of energy helps the electron to come out of the metal surface.
  • This part of energy is equal to the work function of the metal.

 

Purpose-02:

 

  • The remaining part of energy is used in giving a velocity to the emitted photoelectron.
  • This part of energy is equal to the kinetic energy of the emitted photoelectron.

 

According to the law of conservation of energy,

 

 

If ν = ν0 (threshold frequency), then-

  • The free electron is just emitted from the metal surface.
  • But kinetic energy of the electron remains 0.

 

So, above equation may be written as-

0 = W + 0

∴ hν0 = W

 

Using W = hν0 in the above equation, we get-

 

 

The above equation is known as Einstein’s Photoelectric Equation.

 

This equation shows that-

  • Kinetic energy is directly proportional to the frequency.
  • Kinetic energy is inversely proportional to the wavelength.

 

Important Graphs-

 

By Einstein’s photoelectric equation,

hν = W + K.E.

∴ K.E. =  hν – W

 

On comparing with y=mx+c, we get-

m = h and c = -W

 

The following graph shows the variation of kinetic energy of photoelectron with the frequency of incident light-

 

 

For all the metals,

  • The slope remains the same.
  • This is because slope = h which represents plank’s constant and is same for all.

 

 

Laws of Photoelectric Emission-

 

The following laws govern the phenomenon of photoelectric emission-

 

Law-01:

 

For a given substance,

  • There is a minimum frequency of incident light below which no photoelectric emission occurs.
  • This minimum frequency is called as threshold frequency.
  • Below threshold frequency, no photoelectric emission occurs whatever the intensity of light may be.

 

Law-02:

 

  • Number of photoelectrons emitted per second ∝ Intensity of incident light.
  • This is true provided frequency of incident light is greater than threshold frequency.

 

Law-03:

 

  • Kinetic Energy of photoelectrons ∝ Frequency of incident light.
  • This is true provided frequency of incident light is greater than threshold frequency.
  • Kinetic energy of photoelectrons is independent of the intensity of incident light.

 

Law-04:

 

  • The process of photoelectric emission is instantaneous.
  • As soon as the light of suitable frequency is incident on the substance, it emits the photoelectrons.
  • There is no significant delay in emitting the photoelectrons.

 

To gain better understanding about Photoelectric Effect,

Watch this Video Lecture

 

Next Article- Photoelectric Cell

 

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Photoelectric Effect | Einstein's Equation
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Photoelectric Effect | Einstein's Equation
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Photoelectric Effect is a phenomenon of emission of electrons from metal surfaces exposed to light energy of suitable frequency. Einstein's Photoelectric Equation and Laws of Photoelectric Emission are explained.
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