Question

When the wavelength of radiation falling on a metal is changed from $500nm$ to $200nm$, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:

• A. $1.02eV$
• B. $0.61eV$
• C. $0.52eV$
• D. $0.81eV$

Answer 1

The correct option is B

$0.61eV$

Explanation for correct answer:

1. Given that the wavelengths are $$\begin{gathered} {\lambda }_1=500nm \\ {\lambda }_2=200nm \end{gathered}$$

2. According to Einstein's photo electric equation, if $K{E}_{max}$ is the maximum kinetic energy of the emitted photoelectrons, h is the planck's constant and $\varphi$ is the work function of the metal then,

$$\begin{gathered} K{E}_{max}=\frac{hc}{{\lambda }_1}-\varphi \\ 3K{E}_{max}=\frac{hc}{{\lambda }_2}-\varphi \end{gathered}$$

3. Equating the above two equations,

$3\frac{hc-\varphi }{{\lambda }_1}=\frac{hc-\varphi }{{\lambda }_2}$

$\frac{3hc}{{\lambda }_1}-\frac{hc}{{\lambda }_2}=2\varphi$

$\frac{3\times 1240}{500}-\frac{1240}{200}=2\varphi$

solving the above equation we get,

$\varphi =0.619$

Therefore, the work function of a given metal is $0.619eV$.

Hence, option (B) is the right answer.