Question

When the light of frequency $2{\nu }_0$ (where ${\nu }_0$ is a 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 $5{\nu }_0$, 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. 4 : 1
• D. 2 : 1

Answer 1

The correct option is A 1 : 2

From Einstein's equation of photoelectric,
$\frac{1}{2}m{v_1}^2=2h{\nu }_0–h{\nu }_0.............\left(1\right)\frac{1}{2}m{v_2}^2=5h{\nu }_0–h{\nu }_0..............\left(2\right)\left(1\right)÷\left(2\right)\frac{v_1}{v_2}=\sqrt{\frac{1}{4}}=\frac{1}{2}$