Question

Threshold wavelength of Cesium is $\lambda$. Find threshold frequency of Lithium.
Given: work function of Cesium $=1.9\text{eV}$
work function of Lithium $=2.5\text{eV}$
$c$ is the speed of light (photon).

• A. $\frac{19c}{25\lambda }$
• B. $\frac{25c}{19\lambda }$
• C. $\frac{c}{\lambda }$
  
• D. $c\lambda$

Answer 1

The correct option is B $\frac{25c}{19\lambda }$

Work function of Cesium $={\varphi }_C=1.9=\frac{hc}{\lambda }......\left(1\right)$
Work function of Lithium $={\varphi }_L=2.5=h\nu ......\left(2\right)$

Dividing $\left(1\right)$ with $\left(2\right)$,

$\frac{1.9}{2.5}=\frac{c}{\lambda \nu }$

$\therefore \nu =\frac{c}{\lambda }\times \frac{2.5}{1.9}$

$\nu =\frac{25c}{19\lambda }$

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

Why this question? This question tests knowledge of threshold frequency as well as threshold wavelength simultaneously. Note: Option $\left(D\right)$ is dimentionally wrong. $\therefore$ Straight away eliminated.