Question

How do you convert from joules to electron volts?

Answer 1

Hint: You could recall the definition of one electron volt and then use the expression for energy of a charge accelerated across a potential difference to get the expression for 1eV. Thus, you will get the value of 1eV in terms of joules and then you could easily derive the conversion of joules to electron volts from the same.

Formula used:
Energy,
$E=qV$

Complete Step by step solution:
In the question, we are asked to convert joules to electron volts. In order to do that, let us recall the definition of one electron volt.

You may recall that one electron volt is known to be the energy that is required by an electron when that electron is accelerated across 1 volt potential difference. We know that the energy of some charge q that passes through a potential difference V is given by,
$E=qV$

When an electron passes through a potential difference of 1V, the energy could be given by,
$E=e\left(1V\right)$
Where, e is the charge of an electron given by,
$e=1.6\times {10}^{-19}C$
$\Rightarrow E=1.6\times {10}^{-19}C\times 1V$
$\therefore 1eV=1.6\times {10}^{-19}J$ ……………………………………. (1)
Therefore, we found that one electron volt is equivalent to $1.6\times {10}^{-19}$ joules.

We could define one joule of energy as the energy that is required by 1C charge to accelerate across a potential difference of 1 volt. So, from (1) we have,
$1eV=1.6\times {10}^{-19}J$
$\Rightarrow 1J={\displaystyle \frac{1}{1.6\times {10}^{-19}}}eV$
$\therefore 1J=6.25\times {10}^{-18}eV$

Therefore, we found that any given value in joules can be converted to electron volts just by multiplying with $6.25\times {10}^{-18}$.

Note:
Electron volt is considered to be a common unit of energy that has wide applications in particle physics, nuclear physics, atomic physics and solid state physics. The metric prefixes that we use with other units can also be used in case of electron volts. One should always remember that though volt is the SI unit of potential difference, electron volt is not the SI unit of energy.