The spin-only magnetic moment of the Fe²⁺ ion is calculated by first determining the number of unpaired electrons, then applying the spin-only formula. For the Fe²⁺ ion, this calculation yields approximately 4.90 B.M.
Understanding Spin-Only Magnetic Moment
The magnetic properties of transition metal ions primarily arise from the spin of their unpaired electrons. The spin-only magnetic moment provides a good approximation of the total magnetic moment, especially for first-row transition metals where the orbital contribution to magnetism is often quenched. This value is expressed in Bohr Magnetons (B.M.).
The formula for the spin-only magnetic moment (μ) is:
μ = √[n(n+2)] B.M.
Where 'n' represents the number of unpaired electrons in the ion.
Step-by-Step Calculation for Fe²⁺
To calculate the spin-only magnetic moment for the Fe²⁺ ion, follow these steps:
1. Determine the Electronic Configuration of Fe²⁺
First, identify the electronic configuration of a neutral iron atom and then for its Fe²⁺ ion.
- Neutral Iron (Fe): Iron has an atomic number of 26. Its ground state electronic configuration is [Ar] 3d⁶ 4s².
- Fe²⁺ Ion: When iron forms a 2+ ion, it loses two electrons. These electrons are always lost from the outermost 's' orbital first. Therefore, the two electrons are removed from the 4s orbital.
- The electronic configuration of Fe²⁺ is [Ar] 3d⁶.
2. Identify the Number of Unpaired Electrons
Next, visualize the distribution of the 3d electrons in their respective orbitals. A d subshell has five orbitals, and according to Hund's rule, electrons will singly occupy each orbital before any orbital is doubly occupied.
- For the 3d⁶ configuration of Fe²⁺:
- Place one electron in each of the five d orbitals: ↑ ↑ ↑ ↑ ↑
- Place the sixth electron by pairing it with one of the existing electrons: ↑↓ ↑ ↑ ↑ ↑
- By doing this, we can see there are 4 unpaired electrons in the Fe²⁺ ion. So, n = 4.
3. Apply the Spin-Only Magnetic Moment Formula
Finally, substitute the number of unpaired electrons (n=4) into the spin-only magnetic moment formula:
μ = √[n(n+2)] B.M.
μ = √[4(4+2)] B.M.
μ = √[4(6)] B.M.
μ = √24 B.M.
μ ≈ 4.90 B.M.
This table summarizes the calculation for Fe²⁺:
| Step | Description | Result for Fe²⁺ |
|---|---|---|
| 1 | Determine Electronic Configuration | [Ar] 3d⁶ |
| 2 | Identify Unpaired Electrons (n) | 4 unpaired electrons |
| 3 | Apply Spin-Only Formula | μ = √[4(4+2)] = √24 ≈ 4.90 B.M. |
Why Spin-Only?
While the spin-only formula provides a good approximation, it's important to note that the total magnetic moment can also include an orbital contribution. However, in many first-row transition metal complexes, the ligands surrounding the metal ion quench the orbital angular momentum, making the spin-only contribution dominant and a highly accurate estimate.
For more information on electron configuration, you can refer to Wikipedia's article on Electron Configuration. To learn more about magnetic moments in chemistry, Chem LibreTexts provides detailed explanations.
