Question

The substances which contain species with unpaired electrons in their orbitals behave as paramagnetic substances. Such substances are weakly attracted by the magnetic field. Paramagnetism is expressed in terms of magnetic moments. The magnetic moment is related to the number of unpaired electrons according to the following relation :
Magnetic moment, $\mu = \sqrt{n(n+2)} BM$
Where, n = number of unpaired electrons.
BM stands for Bohr magneton, a unit of magnetic moment,
$1BM = \dfrac{eh}{4 \pi mc} = 9.27 \times 10^{ -24 } Am^2orJT^{-1}$
In which of these options do both constituents of the pair have the same magnetic moment ?
(A) $Zn^{2+}$ or $Cu^+$
(B) $Co^{2+}$ or $Ni^{2+}$
(C) $Mn^{2+}$ or $Co^{2+}$
(D) $Mg^{2+}$ or $Sc^+$

Answer 1

To solve the given question, the concepts to be cleared are about Quantum number, shells, sub-shells, orbitals, Pauli Exclusion Principle, Aufbau Rule and P fund's Rule.
Quantum number is basically the address of an electron in an atom.Shells are the permitted orbits where an electron revolves with fixed angular momentum. Subshell is a division under a shell which contains orbital or orbitals.
The four quantum numbers are Principal Quantum Number which denotes the shell, Azimuthal Quantum Number denoting sub-shell, Magnetic Quantum Number and Spin Magnetic Number.
The sub-shells are s,p,d,f, . . . . . . and so on. They are filled on the basis of energy with the $n+l$ rule.

Complete answer:
Step-1 :
Here, we have to find the magnetic moment of the elements which can be directly considered as the number of unpaired electrons. Those elements having the same number of unpaired electrons will have the same magnetic moment.

Step-2 :
The option (A) is $Zn^{2+}$ or $Cu^+$. The atomic number of zinc is $30$. So, its electronic configuration is $1s^22s^22p^63s^23p^63d^{10}$ and has no unpaired electrons. Atomic number of copper is $29$ . So, $Cu^+$ also has the same configuration as $Zn^{2+}$ . So, they both have the same magnetic moment.

Step-3 :
Similarly, in option (B). $Co^{2+}$ or $Ni^{2+}$ contain atomic numbers $27$ and $28$ respectively. So,electronic configuration of $Co^{2+}$ is $1s^22s^22p^63s^23p^63d^7$ and electronic configuration of $Ni^{2+}$ is $1s^22s^22p^63s^23p^63d^8$ . $Co^{2+}$ has $3$ unpaired electron and $Ni^{2+}$ has $2$ unpaired electron. So, their magnetic moment will not be the same.

Step-4 :
In case of option (C), we have the electronic configuration of $Mn^{4+}$ as $[Ar]3d^3$ and $Co^{2+}$ as $[Ar]3d^7$ . They both have $3$ unpaired electrons and so have the same magnetic moment.

Additional Information:
Pauli’s Exclusion Principle states that any $2$ electron can never have all the same $4$ quantum numbers.
Aufbau Rule explains the filling of electrons according to energy level.
P fund’s Rule explains that every orbital has one electron rather than filling another electron.
The magnetic quantum number differentiates orbitals in a given subshell. The l is always less than shell when $l=0,s;l=1,p;l=2,d;l=3,f;$ and so on.
$2$ Electrons are present in s, $6$ in p, $10$ in d and $14$ in f.

Note:
During the electronic configuration, always make sure to write with inner to outer shells but fill the electron according to energy. The energy of $3d$ is more than $4s$ but $3d$ is written inner to $4s$ .