E.1.5—Photon energy

Use the photon relation

Photon energy depends on frequency. For an atomic transition, first take the positive magnitude of the energy-level difference, then convert units consistently before finding frequency or wavelength.

Worked example — hydrogen transition

A transition with $E_\gamma=1.89\,\mathrm{eV}$ has energy $(1.89)(1.60\times10^{-19})=3.02\times10^{-19}\,\mathrm{J}$. Hence $f=E/h=(3.02\times10^{-19})/(6.63\times10^{-34})=4.56\times10^{14}\,\mathrm{Hz}$ and $\lambda=c/f=6.58\times10^{-7}\,\mathrm{m}$.

Connect energy to a level gap

For an atomic transition, use $E_\gamma=|E_i-E_f|$. Take the magnitude of the energy difference, then convert units consistently before finding frequency or wavelength.

Predict the wavelength

A larger energy gap gives a higher-frequency photon and a shorter wavelength. Therefore the longest wavelength comes from the smallest non-zero transition energy.

Common trap

Do not carry a negative sign from bound-state energies into photon energy. The photon energy is positive and equals the magnitude of the level difference.