Question

Two radiations of photons energies $1\text{eV and}25\text{eV}$, successively illuminate a photosensitive metallic surface of work function $0.5\text{eV}$. The ratio of the maximum speeds of the emitted electrons is

• A. $1:2$
• B. $1:4$
• C. $1:1$
• D. $1:5$

Answer 1

The correct option is A $1:2$

Given-
$E_1=h{v}_1=1\text{eV}$, $E_2=h{v}_2=25\text{eV}$,

$\varphi =0.5\text{eV}$

We know that,

$\frac{1}{2}m{V}_{max}^2=hv-\varphi$

$\Rightarrow \frac{(V_1{)}_{max}}{(V_2{)}_{max}}=\frac{\sqrt{h{v}_1-\varphi }}{\sqrt{h{v}_2-\varphi }}=\frac{\sqrt{1-0.5}}{\sqrt{25-0.5}}=\sqrt{\frac{0.5}{2}}=\frac{1}{2}$

Hence, $\left(C\right)$ is the correct answer.