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# What were the principal quantum numbers of the initial and intermediate excited states involved?

Submitted by ahmeded on Thu, 05/10/2012 - 21:10

an electron in an excited state of a hydrogen atom emits two photos in succession the frist at 1817nm and the second at 97.20nm to return to the ground state (n=1) .

for a given transition the wavelengths of the emitted photon corresponds to the difference in energy between the two energy levels.

what were the principal quantum numbers of the initial and the intermediate excited states involved?

You need to apply the Rydberg equation to find the energy levels starting with the second emission where the transition is from n (greater than 1 level to the n=1 level. This will determine were the QN of the middle transition starts (n2 in this case). Then use this value as the lower level to find the QN of the upper level. The formula is from Wikipedia. Remember that n1 is the lower level and n2 the upper level.  Watch out for units of wavelength and R (often in metres-1)

http://en.wikipedia.org/wiki/Rydberg_formula

$\frac{1}{\lambda_{vac}} = R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$