Question

The magnetic moment is associated with its spin angular momentum and orbital angular momentum. Spin only magnetic moment value of $C{r}^{3+}$ ion is ___________.

• A. $3.57B.M.$
• B. $3.47B.M.$
• C. $2.87B.M.$
• D. $3.87B.M.$

Answer 1

The correct option is D $3.87B.M.$

Calculating the number of unpaired electrons in $C{r}^{3+}$ ion :

The electronic configuration of $Cr$ in its $+3$ oxidation state $\left(\text{i.e.}C{r}^{3+}\right)$ is $\left[Ar\right]3d^3.$

So, the number of unpaired electrons in $C{r}^{3+}$ is $3.$

Calculating the spin only magnetic moment :

Magnetic moment is calculated using the formula :

$\mu =\sqrt{n(n+2)}B.M.$

where, $n$ is the number of unpaired electrons.

For $C{r}^{3+}$, the magnetic moment will be :

$\mu =\sqrt{3(3+2)}B.M.$

$=\sqrt{15}$

$=3.87B.M.$

Thus, the spin only magnetic moment value of $C{r}^{3+}$ ion is $3.87B.M.$

So, option $\left(B\right)$ is the correct answer.