When the light of frequency $2
u_0$ (where $
u_0$ is threshold frequency), is incident on a metal plate, the

Question

When the light of frequency $2
u_0$ (where $
u_0$ is 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 $5
u_0$, the maximum velocity of electrons emitted from the same plate is $v_2$. The ratio of $v_1$ to $v_2$ is

Accepted Answer

Using Einstein's photoelectric equation $E = W_0 + \frac{1}{2}mv^2$. For frequency $2
u_0$, $h(2
u_0) = h
u_0 + \frac{1}{2}mv_1^2 \implies h
u_0 = \frac{1}{2}mv_1^2$ (i). For frequency $5
u_0$, $h(5
u_0) = h
u_0 + \frac{1}{2}mv_2^2 \implies 4h
u_0 = \frac{1}{2}mv_2^2$ (ii). Dividing (i) by (ii), we get $\frac{1}{4} = \frac{v_1^2}{v_2^2}$, so $\frac{v_1}{v_2} = \frac{1}{2}$.

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