How do you convert from joules to electron volts?
Hint: To convert joules to electron volts, recall that one electron volt (eV) is the amount of energy an electron gains when it is accelerated through a potential difference of 1 volt. You can use the formula for the energy of a charged particle moving across a potential difference to establish the conversion between electron volts and joules.
Formula Used:
Energy, [latex]E = q \times V[/latex]
Step-by-Step Solution:
Definition of Electron Volt:
One electron volt (1 eV) is the energy gained by an electron when it moves through a potential difference of 1 volt.
Formula for Energy:
The energy [latex]E[/latex] of a particle with charge [latex]q[/latex]moving across a potential difference [latex]V[/latex] is given by:
[latex]E = q \times V[/latex]
Calculation for 1 eV:
For an electron moving across a potential difference of 1 volt, the energy is:
[latex]E = e \times 1 \, \text{V}[/latex]
where [latex]e[/latex] (the charge of an electron) is [latex]1.6 \times 10^{-19}[/latex] coulombs.
Thus:
[latex]E = 1.6 \times 10^{-19} \, \text{C} \times 1 \, \text{V}[/latex]
[latex]∴ 1eV[/latex] = [latex]1.6 \times 10^{-19} \, \text{J}[/latex]
Conversion Factor:
From the above, we find that 1 joule is equivalent to:
[latex]1 \, \text{J} = \frac{1}{1.6 \times 10^{-19}} \, \text{eV}[/latex]
[latex]∴ 1J = 6.25 \times 10^{18} \, \text{eV}[/latex]
So, to convert any energy value from joules to electron volts, multiply by [latex]6.25 \times 10^{18}[/latex].
Note:The electron volt is a commonly used unit of energy in fields like particle physics and atomic physics. While the volt is the SI unit of potential difference, the electron volt is a non-SI unit of energy.