Question

Magnetic moment $2.84BM$ is given by:
(Atomic numbers : $Ni = 28,Ti = 22,Cr = 24,Co = 27$ )
A.$C{r^{ + 2}}$
B.$C{o^{ + 2}}$
C.$N{i^{ + 2}}$
D.$T{i^{ + 3}}$

Answer 1

The magnetic moment is basically the measure of magnetic properties of an ion. It tells us how much torque is produced by it in a magnetic field. The magnetic moment of an ion depends upon the number of unpaired electrons present in it.

Complete step by step answer:
The magnetic moment is the measure of magnetic properties, it is basically a property of a magnet which interacts with a field and gives a mechanical movement. Magnetic moment is a vector quantity, it tells us how much torque is produced by the field when a magnetic material is placed in it.
Here we are discussing the chemical ions. In chemistry magnetic moments also exist but in a different way. In chemistry the magnetic moment is the same, the measure of magnetic properties but it is calculated from the unpaired electrons. The unpaired electron with the same spin contributes to the magnetic moment of the ion.
The formula to calculate magnetic moment is as follows:
${\mu _{eff}} = \sqrt {n(n + 2)} B.M.$
Where, ${\mu _{eff}}$is the magnetic moment
$n$ is the number of unpaired electrons.
$B.M.$ is the unit of magnetic moment, the full form of $B.M.$is Bohr magneton.
So using this formula we will predict the ion.
We have given the magnetic moment i.e. $2.84BM$
Hence we can calculate the number of unpaired electrons by putting it in the formula.
So, $2.84 = \sqrt {n(n + 2)} B.M.$
$\Rightarrow n = 2$
So the approximate value of $n$ is $2$, hence the number of unpaired electrons are two.
Now we will check, which ion has two unpaired electrons from its electronic configuration.
And we know that the electronic configuration of ion $N{i^{ + 2}}$is $\left[ {Ar} \right]3{d^8}$ and the electron are distributed as $t_{2g}^6e_g^2$ so it has two unpaired electrons.

Hence option (C) is correct .

Note:
Bohr magneton is nothing but the unit of the magnetic moment. The mostly used symbol of Bohr magneton is ${\mu _B}$. The magnetic moment of an electron is dependent on its orbital or spin orbital momentum.