An infrared spectrometer reports four hydrogen lines directly as vacuum wavenumbers: ,

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

An infrared spectrometer reports four hydrogen lines directly as vacuum wavenumbers:

5331.6

7799.3

9139.8

and

9948.1\,\mathrm{cm^{-1}}

(NIST ASD). The gaps between successive lines shrink, and all four lie below

12200\,\mathrm{cm^{-1}}

. ((a)) State which series (

n_1 = 1

2

3

) these lines belong to, and assign an upper level

n_2

to each. ((b)) Fit

R_{\rm H}

from the four lines by computing

\tilde\nu/(1/n_1^2 - 1/n_2^2)

for each and averaging. ((c)) Using your fitted

R_{\rm H}

, find the term values

T_3

T_7

\mathrm{cm^{-1}}

and hydrogen's ionisation energy in eV. Sketch the term diagram: a zero at the ionisation limit, the five terms below it, and an arrow for each measured line.

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