[tqnguy9230]

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Problem 5.6-5.6 – What is the longest & shortest
wavelength line in nanometers in the infrared series for
hydrogen, where m=3?
– Longest = n is the smallest (m+1)
– Shortest = n is the largest (∞)
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I'm just lost. Could anyone help me?
The way my instructor explains it is really confusing.

[Schrödinger]

The least energy gap in that series is between n=3 and n=4... The largest would be between the levels n=3 and n=∞.

You also know that E=hc/(wavelength)

Hence, wavelength is inversely proportional to the energy (or energy difference, as is the case here)

[cheese (MSW)]

Use the Rydberg Eqn:
1/ λ  =  R [1/n1^2   -  1/n2^2]
Where λ is the wavelength of the light;
R is the Rydberg constant:  R = 1.09737x 10^7m^-1
n1 and n2 are integers such that n1 < n2  (n1 (n) = 3; n2 (m) = 4,5 ...∞)
Then check your answer (Paschen Series) Ref 3 and
determine which lines are in the near IR λ>~750 -~1500 nm
[1] http://en.wikipedia.org/wiki/Rydberg_formula
[2] http://en.wikipedia.org/wiki/Rydberg_constant
[3] http://en.wikipedia.org/wiki/Hydrogen_spectral_series
[4] http://www.chemguide.co.uk/atoms/properties/hspectrum.html