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. $\mathrm{n}=1,1=0, \mathrm{~m}_{1}=0$ B. $\mathrm{n}=2,1=0, \mathrm{~m}_{1}=0$ C. $\mathrm{n}=2,1=1, \mathrm{~m}_{1}=1$ D. $\mathrm{n}=3,1=2, \mathrm{~m}_{1}=1$ E. $\mathrm{n}=3,1=2, \mathrm{~m}_{1}=0$ Choose the correct answer from the options given below :

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Atomic Structure

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, 1 = 0, m_{1} = 0

n = 2, 1 = 0, m_{1} = 0

n = 2, 1 = 1, m_{1} = 1

n = 3, 1 = 2, m_{1} = 1

n = 3, 1 = 2, m_{1} = 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✓ Correct

Answer: (D)

Solution

In a multielectron atom, orbital energy depends on both

n

and

l

, and true degeneracy (same energy with no external field) requires identical

n

and

l

, differing only in

m_{l}

. Sorting the given sets: A is 1s, B is 2s, C is 2p, while D (

n = 3, l = 2, m_{l} = 1

) and E (

n = 3, l = 2, m_{l} = 0

) are both 3d orbitals differing only in

m_{l}

. D and E share the same

n

and

l

and are therefore degenerate.

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Atomic Structure

Solution

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