Question

The valence electrons of magnesium are different in quantum number.
A. m
B. n
C. I
D. s

Answer 1

Hint: Electronic distribution of an atom/ion is an arrangement in a space of the electrons around the center of the mass(nucleus) of the atom or ion among the orbits or shells. This electronic distribution defines the chemical properties of the atoms.

Complete step by step solution:
The possible values of four quantum numbers are,
Principle quantum number (n) where the value is, $$n=1,2,3,4...$$ any integer.
Azimuthal quantum number (l) the value is, $$l=0-(n-1)$$
Example: for the value for the value of $$\text{n = 3}$$ the value of $$\text{l = 0,1,2}$$ , Where, $$\text{l = 0}$$ for s orbital, $$l=1$$ for p orbital $$l=2$$ for d orbital, $$l=3$$ for f orbital.
Magnetic quantum number (m): the value is $$m=-lto+l$$
Example: for the value $$l=3$$
$$m=-3,-2,-1,0,+1,+2,+3$$
Spin quantum number(s):the value is $$\pm {\displaystyle \frac{1}{2}}$$. for every value of m.
Example: for $$\text{m = - 3, - 2, - 1,0, + 1, + 2, + 3 }$$
$$s=\pm {\displaystyle \frac{1}{2}},\pm {\displaystyle \frac{1}{2}},\pm {\displaystyle \frac{1}{2}},\pm {\displaystyle \frac{1}{2}},\pm {\displaystyle \frac{1}{2}},\pm {\displaystyle \frac{1}{2}},\pm {\displaystyle \frac{1}{2}}$$
Where the + sign means clockwise spin rotation of electron and – sign means anti clockwise spin rotation of electrons.
The electronic distribution of the valence shell of magnesium is $$\left[Ne\right]3s^2$$. Therefore according to the Pauli's exclusion principle there at least one quantum number would be different.
The quantum numbers for the electrons of the valence shell are, $$n=3,l=0,m=0,s=+{\displaystyle \frac{1}{2}}$$ and $$n=3,l=0,m=0,s=-{\displaystyle \frac{1}{2}}$$. These values, the different quantum numbers, are spin quantum numbers.

So, the correct option is, D.

Note:
There are some rules or principles by which an electronic distribution can be written. Those rules are
A. Aufbau principle: This principle states that electrons occupy the lower energy level before occupying the higher energy level. For example: 2s shell is filled before 2p shell. According to the Aufbau principle the energy of the orbitals depends upon the $$\text{(L + S)}$$ value. Higher the value of $$\text{(L + S)}$$ higher will be the energy of the orbital and vice-versa.
B. Pauli's exclusion principle: Any two electrons from a particular electronic distribution cannot have the same values of four quantum numbers. At least one of them should be different.
C. Hund's rule of maximum multiplicity: Electrons will occupy singly the orbitals with the same energy before filling them in pairs.