Determining the Divalent Ion with a 5.92 BM Magnetic Moment

This article explores the concept of divalent ions with a specific magnetic moment, focusing on the determination of a divalent ion that has a 5.92 Bohr magneton (BM) magnetic moment. We will delve into the mathematical methods used to solve this problem and the underlying principles of magnetic moments in ions.

Understanding Magnetic Moment

The magnetic moment of an ion is a critical measure of its magnetic properties, which are inherently linked to the number of unpaired electrons in the ion's d orbitals. This magnetic moment is influenced by the arrangement and pairing of these electrons, as well as the presence of external magnetic fields.

Calculating Magnetic Moment

The calculation of magnetic moment in an ion can be approached using the spin-only formula, which is given by:

[mu sqrt{n(n 2)}]

Where:

(mu) magnetic moment in Bohr magnetons (BM)

n number of unpaired electrons

This formula simplifies the complex interactions of electrons to determine the overall magnetic moment of the ion under consideration.

Analyzing the Given Magnetic Moment

A magnetic moment of 5.92 BM indicates a fairly high number of unpaired electrons. This is important because it suggests the presence of strong magnetic interactions within the ion, which can be useful in various scientific applications, such as in spectroscopy and solid-state physics.

Determining the Divalent Ion

To find the divalent ion corresponding to this magnetic moment, we need to consider the electron configurations of divalent ions and their corresponding number of unpaired electrons. We start by solving the equation derived from the spin-only formula:

[mu 5.92 sqrt{n(n 2)}]

Squaring both sides:

[5.92^2 n(n 2)] [35.0464 n^2 2n]

This results in a quadratic equation:

[n^2 2n - 35.0464 0]

We use the quadratic formula to solve for (n):

[n frac{-b pm sqrt{b^2 - 4ac}}{2a}]

Here, (a 1), (b 2), and (c -35.0464), so:

[n frac{-2 pm sqrt{4 4 times 35.0464}}{2}] [n frac{-2 pm sqrt{144.1856}}{2}] [n frac{-2 12.00776}{2} approx 5.00388]

The negative root is not feasible, so we take the positive value:

[n approx 5]

Towards Identification of the Ion

Given that the ion is a divalent ion and considering its position in the 3d series of the periodic table, the ion in question is likely Manganese(II). The electron configuration of Manganese(II) is as follows:

Electronic configuration: [Ar] 3d5 4s2 Unpaired electrons: 5

Plugging these values into the spin-only formula confirms the magnetic moment:

[n 5][mu sqrt{5(5 2)} sqrt{35} approx 5.92, text{BM}]

This calculation aligns with the given magnetic moment, confirming that the divalent ion with a 5.92 BM magnetic moment is indeed Manganese(II), denoted as Mn2 .

Conclusion

The divalent ion with a 5.92 BM magnetic moment is Manganese(II), or Mn2 . The process of determining this involves understanding the relationship between magnetic moments and the number of unpaired electrons, as well as the specific electron configurations of divalent ions in the 3d series.

Understanding these principles is crucial for researchers and scientists working in fields such as chemistry, physics, and materials science, where the magnetic properties of ions play a significant role.