Question

Work function of metal $A$ is $4.2\text{eV}$. Find the threshold frequency of metal $B$, having work function equal to $80\%$ that of metal $A$.

• A. $5.12\times {10}^{14}\text{Hz}$
• B. $8.145\times {10}^{14}\text{Hz}$
• C. $3.12\times {10}^9\text{Hz}$
• D. $6.67\times {19}^{14}\text{Hz}$

Answer 1

The correct option is B

$8.145\times {10}^{14}\text{Hz}$

Work function is given by, ${\varphi }_0=h{f}_0$

So, for metal $B$, $f_0=\frac{({\varphi }_0{)}_B}{h}=\frac{0.8\times ({\varphi }_0{)}_A}{h}$

$=\frac{0.8\times 4.2\times 1.6\times {10}^{-19}}{6.6\times {10}^{-34}}$

$\therefore f_0=8.145\times {10}^{14}\text{Hz}$

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

Why this question? This question deals with the formula of threshold frequency & work function. (A typical formula based question)