Chapter 27.1, Problem 14PP

To determine

To Find: The work function of the metal.

Answer to Problem 14PP

  $2.92\text{ eV}$

Explanation of Solution

Given data:

Wavelength of incident radiation, $\lambda =193\text{ nm}$

Kinetic energies of electrons, $K.E.=3.5\text{ eV}$

Formula used:

Work function can be obtained by using:

  $\begin{array}{l}\varphi =E-K.E.\\ E=\frac{1240\text{eV}\cdot \text{nm}}{\lambda }\end{array}$

Here, E is the energy of the incident light, h is the Planck’s constant and c is the speed of light. wavelength.

Calculation:

Energy of incident radiation,

  $\begin{array}{l}E=\frac{1240\text{eV}\cdot \text{nm}}{\lambda }\\ E=\frac{1240\text{eV}\cdot \text{nm}}{193\text{nm}}=6.42\text{eV}\end{array}$

  $\varphi =E-K.E.$

  $\begin{array}{l}\varphi =6.42-3.5\\ \varphi =2.92\text{ eV}\end{array}$

Conclusion:

Thus, work function of the metal is $2.92\text{ eV}\text{.}$