For hydrogen atom, the orbital/s with lowest energy is/are : (A) 4 s (B) \(3 \mathrm{p}_{\mathrm{x}}\) (C) \(3 d_{x^{2}-y^{2}}\) (D) \(3 d_{z^{2}}\) (E) \(4 p_{z}\) Choose the correct answer from the options given below :

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Atomic Structure

For hydrogen atom, the orbital/s with lowest energy is/are :
(A) 4 s
(B)

3 p_{x}

(C)

3 d_{x^{2} - y^{2}}

(D)

3 d_{z^{2}}

(E)

4 p_{z}

Choose the correct answer from the options given below :

Answer: (D)

In a hydrogen atom (or any one-electron species), orbital energy depends only on the principal quantum number

n

, because there is no electron–electron repulsion to split the energy by the azimuthal quantum number

l

. All orbitals sharing the same

n

—

3 s, 3 p, 3 d

, or

4 s, 4 p, 4 d, 4 f

— are degenerate.

Among the listed orbitals,

3 p_{x}

3 d_{x^{2} - y^{2}}

and

3 d_{z^{2}}

all belong to

n = 3

and are degenerate with the lowest energy, while

4 s

and

4 p_{z}

belong to the higher

n = 4

shell and lie above them.

The orbitals with lowest energy are

3 p_{x}

3 d_{x^{2} - y^{2}}

and

3 d_{z^{2}}

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Single correct option