Question

Assertion: Magnetic moment of $C{r^{2 + }}$ is higher than that of ${V^{2 + }}$
Reason: The number of unpaired electrons $C{r^{2 + }}$ is higher than ${V^{2 + }}$

Answer 1

To answer this question, you should recall the concept of magnetic moment. Use the rules of electronic configuration to find the number of unpaired electrons and calculate the magnetic moment.

Formula used: $\mu = \sqrt {n\left( {n + 2} \right)} BM$ where$n =$ Number of unpaired electrons

Complete Step by step solution:
The electronic configuration of elements is based on majorly 3 rules:
According to the Pauli Exclusion Principle in an atom, no two electrons will have an identical set or the same quantum numbers. There salient rules of Pauli Exclusion Principle are that only two electrons can occupy the same orbital and the two electrons that are present in the same orbital should be having opposite spins.
According to Hund’s Rule of Maximum Multiplicity rule for a given electronic configuration of an atom, the electron with maximum multiplicity falls lowest in energy.
According to the Aufbau principle, the electrons will start occupying the orbitals with lower energies before occupying higher energy orbitals.
The metal is chromium with atomic number 24. For this atomic number, the valence shell electronic configuration is $3{d^3}4{s^1}$ the number of unpaired electrons in $C{r^{2 + }}$ = 4.
Now we have to calculate the magnetic moment of $C{r^{2 + }}$
$\mu = \sqrt {n(n + 2)} = \sqrt {4(4 + 2)} = 4.89BM$.
${V^{2 + }}$ has an outer electronic configuration of $3{d^3}$ with 3 unpaired electrons. The magnetic moment
$\Rightarrow {\mu _{eff}} = \sqrt {3\left( {3 + 2} \right)} BM = \sqrt {15} BM = 3.87BM$

Hence, both assertion and reason are true and the reason is the correct explanation of the assertion.

Note: The main reason for filling of the electron in $3d$ orbital rather than $4s$ is due to increased stability of half-filled and fully orbitals are:
Symmetrical distribution: Nature loves symmetry as it leads to increased stability and less energy
Exchange energy: The electrons when present in their degenerate orbitals i.e. orbitals with the same energy with parallel spin have shown to exchange their position. The energy released by these exchanges is known as exchange energy. More the exchange of energy and more stability.