Question

Electrons are emitted from the cathode of a photocell of negligible work function, when photons of wavelength  are incident on it. derive the expression for the de broglie wavelength of the electrons emitted in terms of the wavelength of the incident light.

Answer 1

Let de- broglie's wavelength of the emitted electrons = λ₁
And wavelength of incident light = λ₂

Now, according to De - broglie's theory,
λ₁ = h/P
Here P is the momentum of emitted electrons
Let energy of emitted electrons is E
Then, P = √{2mE}, here m is the mass of electrons,
Now, λ₁ = h/√{2mE} --------(1)

According to quantum theory of photoelectrons ,
Energy of incident photons = E = hc/λ₂
Put E = hc/λ₂ in equation (1),
∴ λ₁ = h/√{2m×hc/λ₂}
λ₁² = λ₂h²/(2mhc)

Hence, expression is λ₁² = λ₂h/(2mc)