Question

Write down the values of quantum numbers of all the electrons present in the outermost orbit of argon. (Atomic number 18).

Answer 1

Hint: According to the Bohr's model in the atoms the electron is moving around the nucleus in different shells. These shells are K, L, M, N, etc. These shells are further divided into subshells. K has one subshell, L has two subshells, M has three subshells, N has 4 subshells, and so on.

Complete step by step answer:
Inert gases are from group 18. Which is on the extreme right side of the periodic table. Argon is one of the inert gas the atomic number of argon is 18.
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 of \[{\text{n = 3}}\] the value of \[l = 0,1,2\], Where,\[l = 0\] 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 \[m = - l{\text{ }} to {\text{ }} + l\]
Example: for the value \[l = 3\]
\[m = - 3, - 2, - 1,0, + 1, + 2, + 3{\text{ }}\]
Spin quantum number(s): the value is \[ \pm \dfrac{1}{2}\]. for every value of m.
Example: for \[m = - 3, - 2, - 1,0, + 1, + 2, + 3{\text{ }}\]
\[s = \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}\]
Where the + sign means clockwise spin rotation of electron and the – sign means anti-clockwise spin rotation of electrons.
The electronic distribution of Argon is \[1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}\]. Therefore, according to Pauli's exclusion principle there at least one quantum number would be different.
The valence shell of argon is \[3{s^2}3{p^6}\]. The quantum numbers for each electron of the valence shell \[3{s^2}\] of argon are \[n = 3,l = 0,m = 0,s = + \dfrac{1}{2}, - \dfrac{1}{2}\]
The quantum numbers for each electrons of the valence shell \[3{p^6}\] of argon are
\[n = 3,l = 1,m = 0,s = + \dfrac{1}{2}, - \dfrac{1}{2}\]
\[n = 3,l = 1,m = - 1,s = + \dfrac{1}{2}, - \dfrac{1}{2}\]
\[n = 3,l = 1,m = + 1,s = + \dfrac{1}{2}, - \dfrac{1}{2}\]

Note:
There are some rules or principles by which an electronic distribution can be written. Those rules are
1. Aufbau principle: This principle states that electrons occupy the lower energy level before occupying a higher energy level. For example, the 2s shell is filled before the 2p shell. According to the Aufbau principle the energy of the orbitals depends upon the \[(L + S)\] value. Higher the value of \[(L + S)\] higher will be the energy of the orbital and vice-versa.
2. 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.
3. Hund's rule of maximum multiplicity: Electrons will occupy singly the orbitals with the same energy before filling them in pairs.