question_answer

Magnetic moment 2.83 BM is given by which of the following ions?             (At. No. : Ti = 22; Cr = 24; Mn = 25; Ni = 28)                                                    [AIPMT 2014]

A)  \[T{{i}^{3+}}\]        

B)  \[N{{i}^{2+}}\]

C)  \[C{{r}^{3+}}\]                                 

D)  \[M{{n}^{2+}}\]

Correct Answer: B

Solution :

Magnetic moment is given by \[\mu =\sqrt{n(n+2)}\]

Here, n = number of unpaired electrons

Þ             \[2.83=\sqrt{n(n+2)}\]

Þ             \[{{(2.83)}^{2}}=n(n+2)\]

Þ              \[8.00={{n}^{2}}+2n\]

Þ             \[{{n}^{2}}+2n-8=0\]

Þ             \[{{n}^{2}}+4n-2n-8=0\]

Þ              \[(n+4)(n-2)=0\]

\[\therefore \]      \[n=2\,\,\,\,\,\,\,\,\,\,\,\,\,\,[\because \,n\ne -4]\]

Among the given ions:

Hence, \[N{{i}^{2+}}\] possesses a magnetic moment of

2.83 BM.