The following five hydrogen lines were measured

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · One-electron atoms and the origins of atomic structure

Reading the Spectrum, Ch Lines, series and the term diagram: what a spectrometer measures

Problem

The following five hydrogen lines were measured, the first in vacuum (air absorbs so far into the ultraviolet) and the other four in air:

121.567\,\mathrm{nm}

656.280\,\mathrm{nm}

486.130\,\mathrm{nm}

434.050\,\mathrm{nm}

1875.10\,\mathrm{nm}

. For the visible lines measured in air, use the vacuum correction

\lambda_{\rm vac} = 1.000274\,\lambda_{\rm air}

. ((a)) State which series (Lyman, Balmer or Paschen) each line belongs to, giving your reasoning from the wavelength range alone. ((b)) Convert the three lines you assigned to the Balmer series to vacuum wavenumbers. ((c)) These three Balmer lines correspond to the upper levels

n_2 = 3, 4, 5

(with

n_1=2

). Fit

R_{\rm H}

by computing

\tilde\nu/(1/4 - 1/n_2^2)

for each line and averaging. ((d)) Using your fitted

R_{\rm H}

, construct the term values

T_n = R_{\rm H}/n^2

for

n=1,2,3,4

\mathrm{cm^{-1}}

. Draw them as horizontal lines below a zero marking the ionisation limit, add an arrow for H

\alpha

between the two levels it joins, labelled with its measured wavenumber, and give the ionisation energy of hydrogen in eV.

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