Question

The quantum number of 20th electron of Fe (Z=26) ion would be:
A) 3, 2, -2, -1/2
B) 3, 2, 0, 1/2
C) 4, 0, 0, -1/2
D) 4, 1, -1, 1/2

Answer 1

The electronic configuration of the atom will help find the quantum numbers of the atom. First we need to know what quantum number is. So, a quantum number is a set of numbers used to describe the position and energy of the electron in an atom. There are mainly four quantum numbers which are principal, azimuthal, magnetic and spin quantum numbers.

Complete answer:
Let us discuss these quantum numbers one by one:
Principal quantum number is denoted by n, azimuthal by l, and which is also called orbital angular momentum quantum number, magnetic by $m_l$ and spin by $m_s$ .

Principal quantum number denotes the probable distance between the nucleus and the electrons is described by it. Larger the value of the principal quantum number means greater distance between the electron and the nucleus. The value of this number is always positive.
Azimuthal Quantum number or Orbital Angular Momentum Quantum number describes the shape of a given orbital. Its value is equal to the total number of angular nodes in the orbital. Value of this number indicates either an s, p, d or f subshell which vary in shapes.
Magnetic quantum number determines the total number of orbitals in a subshell and the orientation of the orbitals. This number yields the projection of the angular momentum corresponding to the orbital along a given axis. It is dependent on the value of azimuthal quantum number.
Spin quantum number is independent of the values of other three numbers. This value gives the idea into the direction in which the electron is spinning. The possible values here are 1/2 and -1/2. The positive value implies upward spin on the electron or ‘spin up’ and negative value denotes downward spin or ‘spin down’.
Now, we have all the information so we will calculate the answer.
Electronic configuration of first 19 electrons is $1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^1}$
The 20th electron enters in the 4s shell. So, n = 4
For s orbital l = 0
Magnetic quantum number, $m_l$ = 0
Spin quantum number ${m_s} = - 1/2$

_Therefore, the four quantum numbers are 4, 0, 0, -1/2 which is option C. _

Note: If we write the electronic configuration perfectly then finding the quantum numbers is easy. Just you have to take care while writing the configuration.