Chapter 27, Problem 24P

To determine

Work function of the metal.

Answer to Problem 24P

Solution:

Work function of the metal is $3.46\text{eV}$.

Explanation of Solution

Given:

Wavelength of the UV rays, $\lambda =255\text{nm}=\text{255}\times {\text{10}}^{-9}\text{m}$

Maximum kinetic energy of the electron, $KE=1.40\text{eV}$

Formula used:

The maximum energy of the photon is calculated as

$W=\frac{hc}{e\lambda }$

Here,

$e$ is the charge of electron

$h=6.62\times {10}^{-34}\text{J-s}$ is the Planck’s constant

$c=3\times {10}^8\text{m/s}$ is the speed of light

$\lambda$ is the wavelength

Calculation:

The maximum energy of the photon is calculated as

$W=\frac{hc}{e\lambda }$

Plugging the values in the above equation

$\begin{array}{c}W=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{1.6\times {10}^{-19}\times 255\times {10}^{-9}}\\ =4.86\text{eV}\end{array}$

Since the kinetic energy of the electron is $1.40\text{eV}$, so the work function of the metal is

$\begin{array}{c}E=W-W_o\\ 1.40=4.86-W_o\\ W_o=3.46\text{eV}\end{array}$