JEE Chemistry 2025 Question with Solution

Given: The elements are Sc, Mn, Co and Cu. We must first identify the element with the highest enthalpy of atomisation, and then find the spin-only magnetic moment of its $+2$ oxidation state.

Find: The nearest integer value of the spin-only magnetic moment in BM.

For the given elements, the solution identifies Cobalt (Co) as the element with the highest enthalpy of atomisation because its metallic bonding is strongest among the listed choices. The compared values stated in the solution are: Sc = $326 \, \text{kJ mol}^{-1}$, Mn = $281 \, \text{kJ mol}^{-1}$, Co = $425 \, \text{kJ mol}^{-1}$, Cu = $339 \, \text{kJ mol}^{-1}$.

Now consider the ion $Co^{2+}$. The electronic configuration of neutral cobalt is $[Ar] \, 3d^7 4s^2$. On forming $Co^{2+}$, the two $4s$ electrons are removed, so the configuration becomes $[Ar] \, 3d^7$.

The number of unpaired electrons in $3d^7$ is $n = 3$.

Using the spin-only magnetic moment formula:

Substituting $n = 3$:

Numerically,

So the nearest integer is $4$.

Therefore, the spin-only magnetic moment value is $4$ BM, so the numerical answer is 4.

Given: We compare Sc, Mn, Co and Cu for enthalpy of atomisation, then calculate the magnetic moment of the selected element in the $+2$ oxidation state.

Find: The nearest integer value of the spin-only magnetic moment.

Electronic configurations listed in the solution are:

• Sc: $[Ar] \, 3d^1 4s^2$
• Mn: $[Ar] \, 3d^5 4s^2$
• Co: $[Ar] \, 3d^7 4s^2$
• Cu: $[Ar] \, 3d^{10} 4s^1$

The solution notes that Mn shows a dip in atomisation enthalpy due to the stability of the half-filled $d^5$ configuration, Sc has fewer valence electrons, and Cu has a filled $d$ subshell. Hence Co has the highest enthalpy of atomisation among the given elements.

For $Co^{2+}$:

Removing the two outermost electrons gives:

In a $3d^7$ configuration, five orbitals are filled first singly and then pairing begins. This leaves $3$ unpaired electrons.

Apply the formula:

With $n = 3$:

Rounding to the nearest integer gives $4$. Therefore, the required answer is 4.