The Electronvolt

The energy of a particle with charge $e$ (elementary charge) moving through potential $V$ is given by $E = eV$. Since $e \approx 1.60 \times 10^{-19}$ Coulombs, moving through $1$ Volt results in $1.60 \times 10^{-19}$ Joules.

Conservation of Energy: When an electron is accelerated by an electric field, its electrical potential energy is converted into kinetic energy ($KE$).

This leads to the fundamental conversion factor: $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$

Converting eV to Joules: To convert from electronvolts to Joules, multiply the value by the charge of an electron ($1.60 \times 10^{-19}$). This is necessary when using standard SI formulas like $E = hf$.

Converting Joules to eV: To convert from Joules to electronvolts, divide the value by $1.60 \times 10^{-19}$. This is often done to make final answers more readable in a quantum context.

Prefixes: Because the eV is so small, it is frequently used with metric prefixes: $1 \text{ keV} = 10^3 \text{ eV}$, $1 \text{ MeV} = 10^6 \text{ eV}$, and $1 \text{ GeV} = 10^9 \text{ eV}$.

The SI Rule: Always perform calculations in Joules if the equation involves other SI units (like mass in kg or Planck's constant in J·s). Convert to eV only as a final step if requested.

Sanity Check: If your energy value in Joules is a very small number (e.g., $10^{-18}$), it will likely be a small, 'normal' number in eV (e.g., $1$ to $10$). If you get $10^{-38}$, you likely divided when you should have multiplied.

Speed Calculations: When asked for the speed of an electron given its energy in eV, use the relation $eV = \frac{1}{2}mv^2$. Ensure the energy is converted to Joules before solving for $v$.

Unit Confusion: Students often confuse the unit 'eV' with the variable 'e' (charge) or 'V' (voltage). Remember that 'eV' is a single unit of energy, not a product to be calculated every time you see it.

Incorrect Conversion Direction: A common error is dividing by $1.6 \times 10^{-19}$ when converting eV to Joules. Remember: Joules are 'bigger' units, so the numerical value in Joules must be much smaller than the value in eV.

Mass Units: When calculating velocity from energy in eV, students often forget that the mass ($m$) must be in kilograms (SI), requiring the energy to be in Joules (SI).