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, \(E = q \times V\)
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 \(E\) of a particle with charge \(q\)moving across a potential difference \(V\) is given by:
\(E = q \times V\)
Calculation for 1 eV:
For an electron moving across a potential difference of 1 volt, the energy is:
\(E = e \times 1 \, \text{V}\)
where \(e\) (the charge of an electron) is \(1.6 \times 10^{-19}\) coulombs.
Thus:
\(E = 1.6 \times 10^{-19} \, \text{C} \times 1 \, \text{V}\)
\(∴ 1eV\) = \(1.6 \times 10^{-19} \, \text{J}\)
Conversion Factor:
From the above, we find that 1 joule is equivalent to:
\(1 \, \text{J} = \frac{1}{1.6 \times 10^{-19}} \, \text{eV}\)
\(∴ 1J = 6.25 \times 10^{18} \, \text{eV}\)
So, to convert any energy value from joules to electron volts, multiply by \(6.25 \times 10^{18}\).
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.
