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=(h)/(mv)\Rightarrow v=(h)/(m\lambda)=(6.626*10^(-34))/(9.109*10^(-31)*655*10^(-9))=1110.55(m)/(s)`

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

`(mv^2)/(2)=eV\Rightarrow V=(mv^2)/(2e)=(9.109*10^(-31)*(1110.55)^2)/(2*1.6*10^(-19))=3.51\mu V`

Thus, the voltage is V=3.51uV