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 \[\Rightarrow \]             \[2.83=\sqrt{n(n+2)}\] \[\Rightarrow \]             \[{{(2.83)}^{2}}=n(n+2)\] \[\Rightarrow \]              \[8.00={{n}^{2}}+2n\] \[\Rightarrow \]     \[{{n}^{2}}+2n-8=0\] \[\Rightarrow \]     \[{{n}^{2}}+4n-2n-8=0\] \[\Rightarrow \]              \[(n+4)(n-2)=0\] \[\therefore \] \[n=2\,\,\,\,\,\,\,\,\,\,\,\,\,\,[\because \,n\ne -4]\] Among the given ions: Hence, \[N{{i}^{2+}}\] possesses a magnetic moment of 2.83 BM.