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Determine the correct order of energy for the Li²⁺ species:

A. 3s = 3p = 3d = 4s = 4p
B. 3s = 3p = 3d < 4s = 4p
C. 3s < 3p < 4s < 3d < 4p
D. 3s < 3p < 4s < 4p < 3d

Answer :

In determining the order of energy levels for orbitals in a Li²⁺ ion, the electron configuration and relative energy levels of the orbitals need to be considered.

For Li²⁺, we focus on understanding the energy levels of the orbitals. The electron in a single electron species like Li²⁺ (a hydrogen-like ion) will occupy orbitals based on the principal quantum number (n) and the angular quantum number (l), which determine the energy.

The energy levels for a given principal quantum number (n) in hydrogen-like single electron species are determined as:

  • Orbitals with the same n have the same energy.

Therefore:

  1. For n=3, all orbitals (3s, 3p, and 3d) will have the same energy.
  2. For n=4, all orbitals (4s and 4p) will also have the same energy.
  3. Orbitals with a lower principal quantum number (n) are lower in energy than those with a higher n value.

This means for Li²⁺:

  • 3s = 3p = 3d
  • and 4s = 4p are higher in energy compared to the 3rd shell orbitals.

Thus, option (b) "3s = 3p = 3d < 4s = 4p" is the correct answer, as it properly reflects the energy order of these orbitals in a Li²⁺ ion.

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