Electron volt

Also called eV

An electron volt is a unit of energy, not of voltage. It is the energy an electron gains crossing a potential difference of one volt, equal to 1.60 times 10 to the minus 19 joules.

The AP Physics 2 and AP Physics C: Electricity and Magnetism tables both print 1 eV=1.60×1019 J1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}.

Where the number comes from is worth seeing once, because it settles the confusion in the name. Energy and potential difference are linked by ΔUE=qΔV\Delta U_E = q\,\Delta V. Put in one elementary charge, e=1.60×1019 Ce = 1.60 \times 10^{-19}\ \text{C}, and one volt, and the energy is 1.60×1019 J1.60 \times 10^{-19}\ \text{J}. The unit is a charge times a voltage, and charge times voltage is energy. An electron volt is no more a voltage than a kilowatt hour is a power.

It exists because joules are an awkward size for single particles. Visible photons carry a few eV, and atomic ionisation energies run to tens of eV. The AP Physics 2 sheet supports working directly in these units, printing h=4.14×1015 eVsh = 4.14 \times 10^{-15}\ \text{eV}\cdot\text{s} alongside the value in joule seconds, and hc=1240 eVnmhc = 1240\ \text{eV}\cdot\text{nm}. That last one is the shortcut worth memorising: a 500 nm500\ \text{nm} photon carries 1240/500=2.48 eV1240/500 = 2.48\ \text{eV}.

Two traps. Convert to joules before using any equation that mixes in kilograms and metres, such as K=12mv2K = \tfrac{1}{2}mv^2. And MeV/c2\text{MeV}/c^2, as in 1 u=931 MeV/c21\ \text{u} = 931\ \text{MeV}/c^2, is a unit of mass, not energy.

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