JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Modern Physics

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is

v_{1}

. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes

v_{2}

. If

v_{2} = x v_{1}

, the value of

x

will be ______.

Answer: 2

Solution

Using Einstein's photoelectric equation:

h ν = h ν_{t h} + \frac{1}{2} m v^{2}

For the first case (

ν = 2 ν_{t h}

2 h ν_{t h} = h ν_{t h} + \frac{1}{2} m v_{1}^{2}

h ν_{t h} = \frac{1}{2} m v_{1}^{2} ...(1)

For the second case (

ν = 5 ν_{t h}

5 h ν_{t h} = h ν_{t h} + \frac{1}{2} m v_{2}^{2}

4 h ν_{t h} = \frac{1}{2} m v_{2}^{2} ...(2)

Dividing equation (2) by equation (1):

\frac{v _{2}^{2}}{v _{1}^{2}} = \frac{4 h ν _{t h}}{h ν _{t h}} = 4

Therefore:

v_{2} = 2 v_{1}

, so

x = 2

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Integer answer