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The ionisation potential of a hydrogen-like species is 36 eV. Find the excitation energy (in eV) required to excite this species from its ground state to the first excited state. Express your answer as the sum of its digits.

1. 6
2. 7
3. 8
4. 9

Correct answer: 9

Solution

For a hydrogen-like species with ionisation potential IP = 36 eV: IP = Z² * 13.6 eV (energy to remove electron from n=1). Excitation energy from n=1 to n=2: delta_E = IP * (1 - 1/4) = (3/4) * 36 = 27 eV. Sum of digits: 2 + 7 = 9.

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