Question

Calculate spin only magnetic moment of M\(^{2+}\) ion. [atomic number of M = 26] Write condensed electronic configuration of Gadolinium [Z = 64].

Hint:

For calculating magnetic moment, the key is to correctly determine the number of unpaired electrons. For f-block elements like Gadolinium, remember the special stability associated with the half-filled f\(^7\) configuration, which can lead to an electron occupying the 5d orbital instead of the 4f.

Answer 1

Spin-Only Magnetic Moment Calculation
Step 1: Identify the element and its ion.
The element M with atomic number Z = 26 is Iron (Fe). We need to find the magnetic moment for the M\(^{2+}\) ion, which is Fe\(^{2+}\).

Step 2: Write the electronic configurations.
Fe (Z=26): [Ar] 3d\(^6\) 4s\(^2\)
Fe\(^{2+}\): [Ar] 3d\(^6\)

Step 3: Determine the number of unpaired electrons (n).
In the 3d\(^6\) configuration, the electrons are distributed among the five d-orbitals. Following Hund's rule, there will be one pair and four unpaired electrons. So, n = 4.


Step 4: Calculate the magnetic moment (\(\mu\)).
The formula for spin-only magnetic moment is \( \mu = \sqrt{n(n+2)} \) Bohr Magnetons (BM).
\[ \mu = \sqrt{4(4+2)} = \sqrt{4 \times 6} = \sqrt{24} \approx 4.90 \, \text{BM} \]
Condensed Electronic Configuration of Gadolinium Gadolinium (Gd) has an atomic number Z = 64. Its configuration is an exception to the Aufbau principle due to the stability of the half-filled 4f subshell.
The condensed electronic configuration is:
\[ \text{[Xe]} \, 4f^7 \, 5d^1 \, 6s^2 \]