Chapter 27, Problem 9STP

To determine

To Calculate: The energy given to electron in electron volts.

Answer to Problem 9STP

  $3.76\times {10}^{-3}\text{eV}$

Explanation of Solution

Given data:

de Broglie wavelength, $\lambda =20\text{nm}$

Formula used:

The relation between de Broglie wavelength and energy given to electron is:

  $\lambda =\frac{h}{\sqrt{2mE}}$

Where,

  $\lambda =$ de Broglie wavelength

  $h=$ Planck’s constant

  $m=$mass of electron

  $E=$ Energy

Calculation:

Substitute the known values in the given formula and solve:

  $\lambda =\frac{h}{\sqrt{2mE}}$

  $\begin{array}{l}20\times {10}^{-9}\text{=}\frac{6.626\times {10}^{-34}}{\sqrt{2\times 9.11\times {10}^{-31}\times E}}\\ E=6.024\times {10}^{-22}\text{J}\end{array}$

  $\begin{array}{l}1\text{eV}=1.6\times {10}^{-19}\text{J}\\ E=6.024\times {10}^{-22}\text{J}\\ E=\frac{6.024\times {10}^{-22}\text{J}}{1.6\times {10}^{-19}}\\ E=3.76\times {10}^{-3}\text{eV}\end{array}$

Conclusion:

Thus, the energy given to electron is $3.76\times {10}^{-3}\text{eV}$ .