- #1
Kara386
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Homework Statement
These wavelengths are emitted by a hot gas:
18.226, 13.501, 12.054 (in nanometres)
Show that they are consistent with the Balmer series for a hydrogen-like atom.
Which element do they correspond to?
Homework Equations
Rearranged Rydberg formula for hydrogen-like atoms:
##Z^2 = \frac{hc}{\lambda R}(\frac{1}{n^2}-\frac{1}{4})^{-1}##
The Attempt at a Solution
Z is nuclear charge, that's really what I need to find to identify the element, so I rearranged the Rydberg formula to get the above expression.
The only way I can think of to solve this is by trial and error. So I tried subbing in ##n=3## and the first wavelength, and found that that corresponded to ##Z=6##, then ##n=4## and ##n=5## with the next two wavelengths respectively also gave ##Z=6##. But I'm not sure that really satisfies the condition 'show that they are consistent', because I've just guessed n and it happened to work. Is there a better way to solve this?