Question

When the light of frequency 2$v_0$(where $v_0$ is the threshold frequency), is incident on a metal plate the maximum velocity of electrons emitted is $v_1$ .When the frequency of the incident radiation is increased to 5$v_0$.The maximum velocity of electrons emitted from the same plate is $v_2$.The ratio of $v_{1}to{v}_2$ is

• A. 1:2
• B. 1:4
• C. 2:1
• D. 4:1

Answer 1

Answer: (A)

Using Einstein's photoelectric equation$,$

$E=W_0+K_{max}$

when light of frequency$,2v_0$ is incident on a meal plate$,$

$h\left(2v_0\right)=h{v}_0+\frac{1}{2}m{v_1}^2$

$h{v}_0=\frac{1}{2}m{v_1}^2$---------------$\left(1\right)$

when light of frequency$,5v_0$ is incident on a metal plate

$h\left(5v_0\right)=h{v}_0+\frac{1}{2}m{v_2}^2$

$h{v}_0=\frac{1}{2}m{v_2}^2$----------------$\left(2\right)$

Dividing equation $\left(1\right)$ and $\left(2\right)$

$\frac{1}{4}=\frac{\frac{\sqrt{2}}{1}}{\frac{\sqrt{2}}{2}}$

$\therefore \frac{v_1}{v_2}=\frac{1}{2}$

Hence,

option $\left(A\right)$ is correct answer.