Question

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

Answer 1

Hint: In order to solve the given problem first we will see the relation between the magnetic moment of the atom and the number of unpaired electrons in the configuration of that element. Further on the basis of this relation we will find the number of unpaired electrons present for the given element with the required magnetic moment further we will find the element with the same number of unpaired electrons amongst the given option.


Complete step by step answer:
Given that the element has $2.84BM$ magnetic moment.
As we know the relation between the spin only magnetic moment of an element and the number of unpaired electrons in the ion is given as:
${\mu }_{eff}=\sqrt{n\left(n+2\right)}$
In the above relation ${\mu }_{eff}$ represents the effective spin only magnetic moment of the atom.
And in the above relation “n” represents the number of unpaired electrons.
As we know that ${\mu }_{eff}=2.84BM$ .so let us find the value of “n” or number of unpaired electrons.
$$\begin{gathered} \because {\mu }_{eff}=2.84BM \\ \Rightarrow \sqrt{n\left(n+2\right)}=2.84 \\ \Rightarrow n\left(n+2\right)={\left(2.84\right)}^2=8.0656\approx 8 \\ \Rightarrow n\left(n+2\right)=2\times 4 \\ \Rightarrow n=2 \end{gathered}$$

So, the number of unpaired electrons must be 2 for having required magnetic moment.
As we know that $N{i}^{2+}$ has atomic number 28.
So it will have $3d^8$ electronic configuration.
This electronic configuration can also be written in the following manner.
$t_{2g}^6{e}_g^2$

From the above configuration we can see that nickel ions have 2 unpaired electrons which is the requirement to have required magnetic moment.
Hence, magnetic moment $2.84BM$ is given by $N{i}^{2+}$ ion.
So, the correct answer is “Option C”.

Note: In order to solve such types of students must know the general meaning of magnetic moment. The magnetic moment is the magnetic power and orientation of a magnet or other magnetic field generating entity. An object's magnetic dipole moment is conveniently defined in terms of the torque encountered by the object in a given magnetic field. Also students must remember the formula for the magnetic moment of the ion. And also should know the method to find the unpaired electron in the ion.