Question 117: Dual Nature of Matter and Radiation

Question

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 $$5 \mathrm{f}_{0}$$, the maximum velocity of photoelectrons emitted is $$v_{2}$$. The ratio of $$v_{1}$$ to $$v_{2}$$ is :

Accepted Answer

$$
\begin{aligned}
& \frac{1}{2} m v^2=h f-h f_0 \\
& \Rightarrow \frac{1}{2} m v_1^2=2 h f_0-h f_0=h f_0 \\
& 	ext { also, } \frac{1}{2} m v_2^2=5 h f_0-h f_0=4 h f_0
\end{aligned}
$$
taking ratio,
$$
\frac{v_1^2}{v_2^2}=\frac{1}{4} \Rightarrow \frac{v_1}{v_2}=\frac{1}{2}
$$

Answer

$$\frac{v_{1}}{v_{2}}=\frac{1}{2}$$

Answer

$$\frac{v_{1}}{v_{2}}=\frac{1}{16}$$

Answer

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

Answer

$$\frac{v_{1}}{v_{2}}=\frac{1}{8}$$

Dual Nature of Matter and Radiation

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