Question

If photons of frequency v are incident on the surfaces of metals. A & B of threshold frequencies v/2 and v/3 respectively, the ratio of the maximum kinetic energy of electrons emitted from A to that from B is ______.

Options

• 2 : 3

• 3 : 4

• 1 : 3

• `sqrt 3 : sqrt 2`

Answer 1

If photons of frequency v are incident on the surfaces of metals. A & B of threshold frequencies v/2 and v/3 respectively, the ratio of the maximum kinetic energy of electrons emitted from A to that from B is 3 : 4.

Explanation:

Using Einstein’s photoelectric equation:

K_max​ = h(ν − ν₀​)

For metal A:

ν₀ = `ν/2`

K_A ​= `h(ν - ν/2)`

= `(hν)/2`

For metal B: 

ν₀ = `ν/3`

K_B ​= `h(ν - ν/3)`

= `(2 hν)/3`

Ratio K_A​ : K_B​ = `(hv)/2 : (2 hv)/3`

= `1/2 : 2/3`

= 3 : 4