Question

When monochromatic light of frequency v₁ falls on a metal surface, the stopping potential required is found to be V₁. If the radiation of frequency v₂ is incident on the surface, the stopping potential required V₂ is ______. (v₂ > v₁)

विकल्प

• V₁ - `"h"/"e"` (v₂ + v₁)

• V₁ + `"h"/"e"` (v₁ - v₂)

• V₁ + `"h"/"e"` (v₂ - v₁)

• V₁ - `"h"/(2"e")` (v₁ - v₂)

Answer 1

When monochromatic light of frequency v₁ falls on a metal surface, the stopping potential required is found to be V₁. If the radiation of frequency v₂ is incident on the surface, the stopping potential required V₂ is `bbunderline("V"_1 + "h"/"e" ("v"_2 - "v"_1))`.

Explanation:

Let the work function of the metal be ϕ

Stopping potential of the metal is equal to the maximum kinetic energy of the photoelectrons emitted.

∴ eV = K.E_max = hv - ϕ

For frequency v₁ :

eV₁ = hv₁ - ϕ           ...(i)

For frequency v₂ :

eV₂ = hv₂ - ϕ           ...(ii)

From equation (2) - (1) we get,  

e(V₂ ​− V₁​) = hv₂ ​− hv₁

⇒ V₂ ​= V₁ + `"e"/"h"` (V₂ ​− V₁​)