University12 min

Atomic spectra: levels, lines and the Rydberg formula

Compute the wavelength of a hydrogen line along two routes, place it in its series and say whether the transition is allowed.

The essentials

1

The energy levels

En=−13.6 eV×Z2n2E_n = -13.6\ \text{eV} \times \dfrac{Z^2}{n^2} with Z=1Z = 1 for hydrogen. Bound states: E<0E < 0; at E=0E = 0 the electron is removed. Landmarks for H: E1=−13.6E_1 = -13.6; E2=−3.40E_2 = -3.40; E3=−1.51E_3 = -1.51; E4=−0.85 eVE_4 = -0.85\ \text{eV}. Ionisation energy: +13.6 eV+13.6\ \text{eV}. Degeneracy of a level: n2n^2 without spin, 2n22n^2 with it.
2

One line, one transition, one photon

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3

The Rydberg-Ritz formula

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4

The hydrogen series

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5

The selection rules

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