JEE Main 2025 Jan 28 Shift 1, Chemistry Q13: Quantum Numbers

JEE Main2025Jan 28, Shift 1Chemistry

In a multielectron atom, which of the following orbitals described by three quantum numbers with have same energy in absence of electric and magnetic fields?

A. $n = 1, l = 0, m_{l} = 0$
B. $n = 2, l = 0, m_{l} = 0$
C. $n = 2, l = 1, m_{l} = 1$
D. $n = 3, l = 2, m_{l} = 1$
E. $n = 3, l = 2, m_{l} = 0$

Choose the correct answer from the options given below :

A
A and B only
B
B and C only
C
C and D only
D
D and E only

Solution

Identify each orbital from its $(n, l)$ pair:

A: $n = 1, l = 0 \to 1 s$
B: $n = 2, l = 0 \to 2 s$
C: $n = 2, l = 1 \to 2 p$
D: $n = 3, l = 2 \to 3 d$
E: $n = 3, l = 2 \to 3 d$

In a multielectron atom (without external fields), energy depends on both $n$ and $l$ ; orbitals are degenerate only when they share the same $n$ and $l$ . The different $m_{l}$ values do not lift the degeneracy in the absence of electric or magnetic fields.

D and E are both 3 $d$ orbitals (with different $m_{l}$ ), so they are degenerate.

$∴$ Option (4) — D and E only.

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JEE Main 2025 Jan 28 Shift 1, Chemistry Q13: Quantum Numbers

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