Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

Effective magnetic moment of \(\mathrm{Sc}^{3+}\) ion is (a) 0 (b) \(1.73\) (c) \(2.83\) (d) \(3.87\)

Step-by-Step Solution

Answer

The effective magnetic moment of \(\mathrm{Sc}^{3+}\) is 0.

Step 1: Identify the Electron Configuration

The Scandium ion, \( Sc^{3+} \), loses three electrons compared to the neutral atom. Scandium's ground state electron configuration is \( [Ar]3d^14s^2 \). When it loses three electrons, it becomes \( [Ar] \), meaning there are zero 3d electrons.

Step 2: Determine the Number of Unpaired Electrons

Since the electron configuration of Sc^{3+} is [Ar] and there are no 3d electrons, there are no unpaired electrons in this ion.

Step 3: Calculate the Effective Magnetic Moment

The effective magnetic moment (\mu_{eff}) can be calculated using the formula:\(\mu_{eff} = \sqrt{n(n+2)}\), where n is the number of unpaired electrons. Since n = 0 for \( Sc^{3+} \), the effective magnetic moment is:\(\mu_{eff} = \sqrt{0(0+2)} = 0\).

Key Concepts

Electron Configuration

Every element has a unique electron configuration that describes the specific arrangement of electrons around its nucleus. This configuration is based on principles of quantum mechanics. For scandium, which has an atomic number of 21, the ground state electron configuration is \([Ar]3d^14s^2\). This notation means:

• 2 electrons fill the 1s orbital
• 2 electrons fill the 2s orbital
• 6 electrons fill the 2p orbitals
• 2 electrons fill the 3s orbital
• 6 electrons fill the 3p orbitals
• 1 electron in the 3d orbital and 2 electrons in the 4s orbital

When scandium forms a \(Sc^{3+}\) ion, it loses three electrons from its outer shells, specifically the one 3d electron and the two 4s electrons, leading to the electron configuration \([Ar]\). This simplified configuration indicates that all outer shells beyond argon are emptied in the scandium ion.

Unpaired Electrons

Unpaired electrons are significant in determining the magnetic properties of an ion or atom. They are electrons that are alone in an orbital without a paired electron of opposite spin. The fewer electrons there are in outer orbitals, the fewer opportunities for unpaired electrons.
In the case of \(Sc^{3+}\), which adopts the \([Ar]\) electron configuration, there are no electrons in the outer \(3d\) or \(4s\) orbitals. As a result, there are no unpaired electrons.
It's important to remember that because unpaired electrons directly contribute to an element's magnetic moment, the absence of unpaired electrons in \(Sc^{3+}\) leads to no magnetic moment.

Scandium Ion

Scandium ions, particularly the \(Sc^{3+}\) form, play a vital role in understanding electron loss and stability in transition metals. Scandium, a transition metal, often forms ions by losing electrons from its outer orbitals.
The \(Sc^{3+}\) ion results when scandium loses its three outermost electrons: one from the 3d orbital and two from the 4s orbital. This process gives \(Sc^{3+}\) the electron configuration of a noble gas, \([Ar]\), enhancing its stability.
One notable consequence of having the \([Ar]\) configuration is that \(Sc^{3+}\) is diamagnetic. This means it doesn't have a net magnetic field as all electron spins are paired, making it insensitive to external magnetic fields. Overall, understanding the scandium ion helps in comprehending broader concepts of electron transition and ion stability in chemistry.