Question

Magnetic moment of $X^{n+}$ (Z = 26) is $\sqrt{24}$ B.M. Hence number of unpaired electrons and value of n respectively are:
A.4, 2
B.2, 4
C.3, 1
D.0, 2

Answer 1

Hint:The atomic number given is 26 which is the atomic number of element iron (Fe). Also to find the unpaired electron you can go with electronic configuration or magnetic moment.
Formula used: Magnetic moment = $\sqrt{\text{n(n + 2) }}$

Complete step by step answer: Let’s start with discussing a little about the magnetic moment and what it represents. Magnetic moment is the orientation of a magnetic field which is released by a magnet or other objects, similarly atoms have their own magnetic moment. To be more precise the magnetic moment represents the net magnetic dipole moment of the object.
Coming to the question we are given with the atomic number of the molecule which is Z = 26 along with the magnetic moment of the atom which is $\sqrt{24}$ B.M. We are asked to find the number of unpaired electrons along with the value of n in Xn+.
For finding the unpaired electron we will write the electronic configuration and for the atomic number 26 it will be $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^2$, so the last and unfilled orbital is 3d orbital and in 3d orbital there are 5 subshells. There are 6 electrons in 3d orbital and one each will first enter the subshells that means 5 electron and then the last electron will form a pair with the first electron which means that 4 electron will be unpaired.
This can also be solved with magnetic moment, we know, Magnetic moment = $\sqrt{\text{n(n + 2) }}=\sqrt{24}$ (n = unpaired electrons)
This gives unpaired electrons is 4.
Now coming to the value of n, we know that Fe is the molecule having 26 atomic numbers and its oxidation state is 2, so n=2.
Therefore, the option A is correct i.e., 4, 2.


Note: Magnetic moment is a concept on which many scientists are still working and there is much more to find about. We already know that it is the sun's magnetic field which makes the planets revolve around it and it is the earth’s magnetic field which makes it rotate on its axis as well as the climatic conditions are also affected by the magnetic field.