A classmate measures the four visible Balmer lines in air at ,

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

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

Problem

A classmate measures the four visible Balmer lines in air at

656.28

486.13

434.05

and

410.17\,\mathrm{nm}

and writes up a fit of

R_{\rm H}

as follows. "Convert each wavelength with

\tilde\nu\,[\mathrm{cm^{-1}}] = 10^7/\lambda\,[\mathrm{nm}]

: this gives

15237.4

20570.6

23038.8

and

24380.1\,\mathrm{cm^{-1}}

for

n_2 = 3, 4, 5, 6

. Plotted against

1/4 - 1/n_2^2

, the four points lie on a straight line through the origin to within

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

, so the fit is good; its gradient is

R_{\rm H} = 1.0971\times10^5\,\mathrm{cm^{-1}}

." ((a)) Find the error in the procedure, and explain why the straight-line fit still looked convincing. ((b)) Redo the fit correctly, using the chapter's correction

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

, and give

R_{\rm H}

to five significant figures. ((c)) By how many

\mathrm{cm^{-1}}

, to two significant figures, does your classmate's gradient exceed the corrected one?

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