Question

An electron accelerated from a rest position through a potential difference of 30.0V. Find the de Broglie wavelength of the electron after it has passed through the potential difference 

Answer 1

From conservation of energy:

$$PE=KE,\\\space\\ qV=\frac12 mv^2,\\\space\\ v=\sqrt{\frac{2qV}{m}}.$$

De Broglie wavelength of the electron:

$$\lambda=\frac{h}{mv}=\frac{h}{\sqrt{2mqV}}=224\text{ pm}.$$