Chapter 27, Problem 19P

To determine

Longest wavelength that can emit electron from the metal.

Answer to Problem 19P

Solution:

Longest wavelength that can emit electron from the metal is $429\text{nm}$.

Explanation of Solution

Given:

Work function, $E=2.90\text{eV}$

Formula used:

The maximum wavelength is calculated by the formula

$E=\frac{hc}{\lambda }$

Here,

$h=6.62\times {10}^{-34}\text{J-s}$ 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 wavelength is calculated as

$E=\frac{hc}{\lambda }$

Plugging the values in the above equation

$\begin{array}{c}2.90\times 1.6\times {10}^{-19}=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{\lambda }\\ \lambda =429\times {10}^{-9}\text{m}\\ =429\text{nm}\end{array}$

Thus, the longest wavelength that can emit electron from the metal is $429\text{nm}$.