PYQ NEET- Dual Nature Of Matter And Radiation L-6

Question: When the light of frequency $2 v_0$ (where $v_0$ 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 $v_0$, 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) $4: 1$

D) $2: 1$

Answer: $1: 2$#

Solution:#

From Einstein’s equation $$ \frac{1}{2} m v_1^2=2 h \nu_0-h \nu_0=h \nu_0 $$

Again, $\frac{1}{2} m v_2^2=5 h \nu_0-h \nu_0=4 h \nu_0$ $$ \therefore \frac{v_1}{v_2}=\sqrt{\frac{1}{4}}=\frac{1}{2} $$