Question

If the final speed of a free electron accelerated from rest is 5.9.10^6 m/s. Calculate the potential difference through which the electron was accelerated.

Answer 1

-99.1 V

Step-by-step explanation:

For a free electron accelerated from rest, the final kinetic energy of the electron is equal to the change in electric potential energy of the electron:

`K=\Delta U\\(1)/(2)mv^2 = q\Delta V`

where

`m=9.11\cdot 10^(-31)kg` is the mass of the electron

`v=5.9\cdot 10^6 m/s` is the final speed

`q=-1.6\cdot 10^(-19) C` is the charge of the electron

`\Delta V` is the potential difference

Solving for
`\Delta V`, we find

`\Delta V=(mv^2)/(2q)=((9.11\cdot 10^(-31))(5.9\cdot 10^6)^2)/(2(-1.6\cdot 10^(-19)))=-99.1 V`