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  4. The threshold frequency of a metal is f 0. When the light of frequency 2 f 0 is incident on the metal plate, the maximum velocity of photoelectrons is v1. When the frequency of incident radiation is increased to 5 f 0, the maximum velocity of photoelectrons emitted is v2. The ratio of v1 to v2 is :

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Q. The threshold frequency of a metal is $f _0$. When the light of frequency $2 f _0$ is incident on the metal plate, the maximum velocity of photoelectrons is $v_1$. When the frequency of incident radiation is increased to $5 f _0$, the maximum velocity of photoelectrons emitted is $v_2$. The ratio of $v_1$ to $v_2$ is :

JEE MainJEE Main 2023Dual Nature of Radiation and Matter

Solution:

$ K _{\max }= hf - hf _0 $
$ \text { For } f =2 f _0 $
$ \frac{1}{2} m V _1^2=2 h _0- hf _0= hf _0 $
$ \text { For } f =5 f _0 $
$ \frac{1}{2} m V _2^2=5 hf_{0 } - hf f _0=4 hf f _0$
$ \frac{ V _1}{ V _2}=\frac{1}{2} $