JEE Main 2025 Jan 24 Shift 2, Chemistry Q4: Bohr's Atomic Model

JEE Main2025Jan 24, Shift 2Chemistry

For hydrogen atom, the orbital/s with lowest energy is/are :

(A) $4 s$

(B) $3 p_{x}$

(D) $3 d_{z^{2}}$

(E) $4 p_{z}$

Choose the correct answer from the options given below :

A
(A) and (E) only
B
(B) only
C
(A) only
D
(B), (C) and (D) only

Solution

For a one-electron species such as the hydrogen atom, orbital energy depends solely on the principal quantum number $n$ (no $n + l$ splitting because there is no inter-electronic repulsion). All orbitals with the same $n$ are degenerate.

Grouping the listed orbitals by $n$ :

$n = 3$ : $3 p_{x}$ , $3 d_{x^{2} - y^{2}}$ , $3 d_{z^{2}}$ (options B, C, D)

$n = 4$ : $4 s$ , $4 p_{z}$ (options A, E)

The lowest energy set is the $n = 3$ group, so options (B), (C) and (D) are correct.

$∴ E_{3 p_{x}} = E_{3 d_{x^{2} - y^{2}}} = E_{3 d_{z^{2}}} < E_{4 s} = E_{4 p_{z}}$

Correct option: (4)

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JEE Main 2025 Jan 24 Shift 2, Chemistry Q4: Bohr's Atomic Model

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