TPR AP Atomic and Nuclear Physics Example 4 11768

Electrons in a diffraction experiment are accelerated through a potential difference of $200\ \mathrm{V}$.

What is the de Broglie wavelength of these electrons?

$\lambda =0.087\ \mathrm{nm}$

By definition, the kinetic energy of these electrons is 200 eV. Since the relationship between linear momentum and kinetic energy is

$$p=\sqrt{2mK}$$

$$\lambda =\frac{h}{p}$$

$$\lambda =\frac{h}{\sqrt{2mK}}$$

$$\lambda =\frac{6.63\times 10^{-34}\ \mathrm{J\cdot s}}{\sqrt{2\left(9.11\times 10^{-31}\ \mathrm{kg}\right)\left[200\ \mathrm{eV}\cdot \displaystyle \frac{1.6\times 10^{-19}\ \mathrm{J}}{1\ \mathrm{eV}}\right]}}$$

$$\lambda =8.7\times 10^{-11}\ \mathrm{m}$$

$$\lambda =0.087\ \mathrm{nm}$$

This wavelength is characteristic of X‑rays.