JEE Main 2024 · 30 January · morning · Single correct · +4 / −1
Given below are two statements :
Statement (I) : The orbitals having same energy are called as degenerate orbitals.
Statement (II) : In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals.
In the light of the above statements, choose the most appropriate answer from the options given below :
- (a) Statement I is true but Statement II is false
- (b) Statement I is false but Statement II is true
- (c) Both Statement I and Statement II are false
- (d) Both Statement I and Statement II are true
Answer and solution
Answer (a) Statement I is true but Statement II is false
Solution
Chemistry ma’am · 4 steps
In hydrogen, energy depends only on n, so every orbital in the same shell has the same energy.
- Statement I. Degenerate orbitals are orbitals with the same energy. That is the definition, so Statement I is true.
- Energy in hydrogen. Hydrogen has only one electron, so there is no electron–electron repulsion and no shielding. Its orbital energy depends on the principal quantum number n alone.
Eₙ = -13.6/n² eV
- Statement II. For n = 3, the 3s, 3p and 3d orbitals all have E₃ = -13.6/9 = -1.51 eV. So 3p and 3d are degenerate in hydrogen, and Statement II is false.
- So. Statement I is true and Statement II is false, which is option (a).
The idea to keep. One-electron species (H, He⁺, Li²⁺): energy depends on n only. Multi-electron atoms: energy depends on n + l, so 3s, 3p and 3d split apart.
Answer from the NTA final answer key. Solution by PrepWiser.