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A hydrogen-like atom (atomic number ) is in a higher excited state of quantum number . This excited atom can make a transition to the first excited state by successively emitting two photons of energies and respectively. Alternatively, the atom from the same excited state can make a transition to the second excited state by successively emitting two photons of energy and respectively. Determine the values of and .
(a)
(b)
(c)
(d)

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Important Questions on Atomic Structure
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For any given series of spectral lines of atomic hydrogen, let be the difference in maximum and minimum wave number in .
The ratio is

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Draw the energy level diagram of the hydrogen atom and show transitions responsible for emission lines of the Balmer series.

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(i) As ware length decreases, the lines in the series converge
(ii) The integer is equal to
(iii) The ionization energy of hydrogen can be calculated from the wave number of these lines
(iv) The line of longest wavelength corresponds to

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