JEE Chemistry 2025 Question with Solution

Given: The orbitals are specified by $n$, $l$, and $m_l$ for a multielectron atom in the absence of electric and magnetic fields.

Find: Which orbitals have the same energy.

In a multielectron atom, in the absence of electric and magnetic fields, the energy of an orbital depends only on the principal quantum number $n$ and the azimuthal quantum number $l$. The magnetic quantum number $m_l$ does not affect the energy under these conditions.

So, compare the given orbitals by their $n$ and $l$ values:

• 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: $n = 3, l = 2, m_l = 0$

Only D and E have the same $n = 3$ and $l = 2$. Their $m_l$ values are different, but that does not change the energy in the absence of external fields.

Therefore, the orbitals with the same energy are D and E only. The correct option is A.

Given: Five orbitals are listed using the three quantum numbers $n$, $l$, and $m_l$.

Find: The pair having equal energy in a multielectron atom without external fields.

Check each orbital identity:

• $n = 1, l = 0$ corresponds to $1s$
• $n = 2, l = 0$ corresponds to $2s$
• $n = 2, l = 1$ corresponds to $2p$
• $n = 3, l = 2$ corresponds to $3d$
• $n = 3, l = 2$ corresponds again to $3d$

Thus, D and E are both $3d$ orbitals. Since only $m_l$ differs between them, they remain degenerate when electric and magnetic fields are absent.

Hence, the final answer is D and E Only, so the correct option is A.