Question

An electron initially at rest is accelerated through a potential difference of $1V$. The energy gained by the electron is:

Answer 1

Step1: Given data

1. The potential difference is $V=1volt.$

Step2: The potential energy of an electron

1. The potential energy of an electron is the work done to bring an electron through a certain potential difference.
2. The potential energy of an electron is defined by the form, $E_p=eV$, where, e is the charge of an electron and V is the certain potential difference.
3. This potential energy will increase the energy of the electron.

Step3: Calculation of energy gain

As we know, $E_p=eV$

So,

$$\begin{gathered} E_p=eV=\left(1.602\times {10}^{-19}\right)\times 1\left(\sin ce,thechargeofelectronis1.602\times {10}^{-19}C\right) \\ or{E}_p=\left(1.602\times {10}^{-19}\right)joule. \end{gathered}$$

Therefore, The energy gained by the electron is $1.602\times {10}^{-19}joule.$