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In a multi-electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic acid and electric fields? (a) n = 1, l = 0, m = 0 (b) n = 2, l = 0, m = 0 (c) n = 2, l = 1, m = 1 (d) n = 3, l = 2, m = 1 (e) n = 3, l = 2, m = 0

1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. (d) and (e)

Correct answer: (a) and (b)

Solution

In a multi-electron atom, orbitals with the same principal quantum number (n) but different angular momentum quantum numbers (l) generally have different energies due to electron-electron interactions. However, the 1s orbital (n=1, l=0) and the 2s orbital (n=2, l=0) are both in their respective shells and do not experience these interactions in the same way, thus they can be considered to have the same energy in the absence of external fields.

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