Q.NO. 14
The azimuthal quantum number (l) of an electron in the dz² orbital of a copper
atom (atomic number: 29) is _______.

The azimuthal quantum number (l) for an electron in the dz² orbital of a copper atom is 2.

This value holds regardless of the atom, as l defines the subshell shape. Copper’s atomic number 29 confirms dz² belongs to its 3d subshell.

Quantum Numbers Basics

Quantum numbers describe electron states in atoms. The azimuthal quantum number l specifies subshell type: l=0 for s, l=1 for p, l=2 for d, l=3 for f.

All d orbitals, including dz², have l=2. The magnetic quantum number ml distinguishes them (ml=0 for dz²).

Copper Electron Setup

Copper (Z=29) has configuration [Ar] 4s¹ 3d¹⁰. The 3d¹⁰ includes two electrons in dz² (n=3, l=2, ml=0).

Principal quantum number n=3 for these electrons. Atomic details do not alter l.

dz² Orbital Details

The dz² orbital features lobes along the z-axis and a ring in the xy-plane. It remains a d orbital with fixed l=2.

No options provided, but common choices are l=0 (s), l=1 (p), l=2 (d, correct), l=3 (f). Others fail as dz² is not s, p, or f.

The azimuthal quantum number dz2 orbital copper atom question tests core quantum mechanics for exams like CSIR NET Life Sciences. Copper (atomic number 29) has electrons in 3d orbitals, including dz².

Why l=2 for dz²?

The azimuthal quantum number l determines orbital shape. D orbitals like dz² always have l=2, with five orientations (ml=-2 to +2). Dz² specifically has ml=0.

In copper’s [Ar] 4s¹ 3d¹⁰ setup, 3d electrons occupy n=3, l=2 subshell.

Option Explanations

• l=0: S orbital (spherical); incorrect for dz².
• l=1: P orbital (dumbbell); wrong subshell.
• l=2: D orbital; matches dz² perfectly.
• l=3: F orbital; too complex, not applicable.

CSIR NET Relevance

This aligns with molecular orbital theory in life sciences. Master l values for electron configurations in transition metals like copper.