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What is the ratio of the total energy of an electron in a hydrogen atom in the first excited state and the third excited state?

Asked in GSEB Board March 2023 · Energy levels and ionisation

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

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 3:1; it is just the ratio of the labels 'third' and 'first'. Sanity check: the states are n=2 and n=4, and E∝1/(n²) gives (16)/4=4, i.e. 4:1.
• (3) 1:1 would mean every level has the same total energy, but Eₙ=-(13.6)/(n²) eV changes with n: -3.4 eV against -0.85 eV here.
• (4) 1:4 is the ratio turned upside down, which is also what taking the energy to grow as n² gives (2²:4²).

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