JEE MAIN - Chemistry (2024 - 30th January Morning Shift - No. 12)

Given below are two statements :

Statement (I) : The orbitals having same energy are called as degenerate orbitals.

Statement (II) : In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals.

In the light of the above statements, choose the most appropriate answer from the options given below :

Statement I is true but Statement II is false
Statement I is false but Statement II is true
Both Statement I and Statement II are false
Both Statement I and Statement II are true

Explanation

Degenerate Orbitals: Orbitals that have the same energy are called degenerate orbitals.

Hydrogen-like Atoms (Single-Electron Systems): In a hydrogen atom (or any one-electron system), the energy of an orbital depends only on the principal quantum number $n$, not on the azimuthal quantum number $l$. Therefore, all orbitals with the same $n$ (e.g., 3s, 3p, 3d) have the same energy and are degenerate.

Multi-electron Atoms: In atoms with more than one electron, the energy also depends on $l$ (and other factors like screening), so 3s, 3p, and 3d orbitals are not all degenerate in multi-electron atoms.

Now, let us evaluate the given statements:

Statement (I): “The orbitals having same energy are called as degenerate orbitals.”

This statement is true by definition.

Statement (II): “In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals.”

In a hydrogen atom, all orbitals with the same principal quantum number $n$ (like 3s, 3p, 3d) are degenerate.

Hence, this statement is false.

Therefore, the correct option is:

Option A: Statement I is true but Statement II is false.

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