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The ratio of energies of the electron in the second excited state to the first excited state in an H-atom is _______.

Asked in GSEB Board July 2018 · Energy levels and ionisation

• (1) 1:4
• (2) 9:4
• (3) 4:9
• (4) 4:4

Step-by-step solution

Why the other options are wrong

• (1) 1:4 counts the excited states from n=1: taking the second excited state as n=2 and the first as n=1 gives 1/(2²):1/(1²)=1:4. The first excited state is n=2.
• (2) 9:4 is the ratio turned upside down, first excited state to second, which is also what taking the energy to grow as n² gives (3²:2²).
• (4) 4:4 puts both states at n=2, reading 'second excited state' as the second orbit. Two different levels cannot have equal energies.

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