Einstein's Equation Of PE Current

Description:

Whenever light is incident on the metal surface, the photon hits the free electron within the metal and transfers its energy to the electron.

Einstein gave an equation for this transfer of energy −

Energy imparted to electron = hv

Energy used as work function = Φ_o = hv₀

Rest of the energy is retained with ejected electron in the form of kinetic energy.

∴ K.E. = hv − Φ_o

K.E. = hv − hv₀

As we know,

K.E. = 1/2 mv²

So,

1/2 mv² = h(v − v₀)

Where,

v = Velocity of light/photon.

v_o = Threshold frequency of metal.

This is known as Einstein’s equation.

Now we have,

v = c/λ

∴ 1/2 mv² = hC(1/λ − 1/λ_o)

Where,

λ = Wavelength of light.

λ_o = Threshold wavelength.

We also have a relationship between kinetic energy and stopping potential −

K.E. = eV₀

Comparing this equation with Einstein’s equation, we get −

eV₀ = hC(1/λ - 1/λ_o)

Where,

e = Charge on electron.

V₀ = Stopping potential.