Question

The deBroglie wavelength, associated with electrons, accelerated through a potential V, equals λ_B . The threshold wavelength, for a given photosensitive surface is λ_B (n > 1) . If this photosensitive surface is irradiated with monochromatic radiation of wavelength (λ_B/n), the stopping potential needed is V_S . 

The relation, between V_S and V, can be expressed as

(1) \(V_s=\left[\frac{(n^2-1)c}{n}\sqrt{\frac{2m}{e}}\right]\sqrt{V}\)

(2) \(V=\left[\frac{nc}{(n^2-1)}\sqrt{\frac{2m}{e}}\right]\sqrt{V}\)

(3) \(V_s=\left[\frac{nc}{(n^2-1)}\sqrt{\frac{2m}{e}}\right]\sqrt{V}\)

(4) \(V=\left[\frac{(n^2-1)c}{n}\sqrt{\frac{2m}{e}}\right]\sqrt{V_s}\)

Answer 1

 (1) \(V_s=\left[\frac{(n^2-1)c}{n}\sqrt{\frac{2m}{e}}\right]\sqrt{V}\)

The work function, of the photosensitive surface = energy of a photon of its ‘threshold wavelength’ radiation = hc/nλ_B

Energy of a photon of the incident radiation

∴ As per Einstein’s photoelectric equation, 

we have 

This is the required relation between V_S and V.