Question

Through what potential difference, in microvolts, must an electron be accelerated from rest to have a de Broglie wavelength of 655 nm?

Answer 1

First, we need to find out the velocity the electron must have, according to the DeBroglie wavelength. This relation can be written as:

$\lambda=\frac{h}{mv}\Rightarrow v=\frac{h}{m\lambda}=\frac{6.626*10^{-34}}{9.109*10^{-31}*655*10^{-9}}=1110.55\frac{m}{s}$

With this velocity, we can find out the voltage through the following relation:

$\frac{mv^2}{2}=eV\Rightarrow V=\frac{mv^2}{2e}=\frac{9.109*10^{-31}*(1110.55)^2}{2*1.6*10^{-19}}=3.51\mu V$

Thus, the voltage is V=3.51uV