JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Modern Physics

The threshold frequency of metal is

f_{0}

. When the light of frequency

2 f_{0}

is incident on the metal plate, the maximum velocity of photoelectron is

v_{1}

. When the frequency of incident radiation is increased to

5 f_{0}

, the maximum velocity of photoelectrons emitted is

v_{2}

. The ratio of

v_{1}

v_{2}

is:

Answer: (A)

Solution

By Einstein's photoelectric equation the maximum kinetic energy is

\frac{1}{2} m v^{2} = h f - h f_{0}

. For

f = 2 f_{0}

\frac{1}{2} m v_{1}^{2} = 2 h f_{0} - h f_{0} = h f_{0}

, and for

f = 5 f_{0}

\frac{1}{2} m v_{2}^{2} = 5 h f_{0} - h f_{0} = 4 h f_{0}

. Dividing,

\frac{v _{1}^{2}}{v _{2}^{2}} = \frac{1}{4}

, so

\frac{v _{1}}{v _{2}} = \frac{1}{2}

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Single correct option