Question

Write the four quantum numbers for the differentiating electron of sodium ${\text{(Na)}}$ atom?

Answer 1

Differentiating electron is the most valence electron in an atom. It is the electron which is which is added last in the atom.

Complete step by step answer:
First of all, let's understand about quantum numbers. Quantum numbers may be defined as a set of four numbers with the help of which we can get complete information about all the electrons in an atom i.e. location, energy, type of orbital occupied, shape and orientation of that orbital etc. These numbers are like the postal address of a man. There are four types of quantum numbers discussed as follows.
${\text{1}}{\text{.}}$ Principal quantum number: It is the most important quantum number since it tells the principal energy level or shell to which the electron belongs. It is denoted by the letter n and can have any integral value except zero. It tells the maximum number of electrons present in any principal shell. Its value is equal to the integer value of the highest subshell in which an electron is present in an atom.
${\text{2}}{\text{.}}$ Azimuthal quantum number: It gives us the number of subshells present in the main shell. It also gives us the angular momentum of the electron present in any subshell. It also provides us the information of relative energies of various subshells and their shapes. This quantum number is denoted by letter l. For a given value of n, it can have an integral value ranging from ${\text{0}}$ to ${\text{n - 1}}$.

Value of l	${\text{0}}$	${\text{1}}$	${\text{2}}$	${\text{3}}$
Designation of sub-shell	s	p	d	f

${\text{3}}{\text{.}}$ Magnetic quantum number: This quantum number is required to explain the fact that when the source producing the line spectrum is placed in a magnetic field is spectral line splits up into a number of lines. It determines the number of preferred orientations of an electron present in a subshell. This quantum number is denoted by letter m. For a given value of l, it can have all values ranging from -l to +l.

Sub-shell	s	p	d	f
Number of orbital present	${\text{1}}$	${\text{3}}$	${\text{5}}$	${\text{7}}$

${\text{4}}{\text{.}}$ Spin Quantum number: This quantum number helps to explain the magnetic properties of the substance. It is denoted by the letter s. Its value is either $\dfrac{{\text{1}}}{{\text{2}}}$ or ${\text{0}}$.
Now we have to find all the four quantum for the differentiating electron of sodium atom. Sodium has an atomic number ${\text{11}}$ and atomic mass ${\text{23 u}}$. Its electronic configuration is ${\text{1}}{{\text{s}}^{\text{2}}}{\text{2}}{{\text{s}}^{\text{2}}}{\text{2}}{{\text{p}}^{\text{6}}}{\text{3}}{{\text{p}}^{\text{1}}}$. The differentiating electron is present in ${\text{3s}}$ orbital. So, the value of the principal quantum number should be ${\text{3}}$ as it is the highest value of the subshell. This electron is present in s orbital so the value of azimuthal quantum number will be ${\text{0}}$ and that of magnetic quantum number is also ${\text{0}}$. Since the s orbital is half filled so the value of spin quantum number should be ${\text{ + }}\dfrac{{\text{1}}}{{\text{2}}}$.
${\text{n = 3, l = 0, m = 0, s = + }}\dfrac{{\text{1}}}{{\text{2}}}$

Note:
In an atom if all the orbitals are fully filled, the net magnetic moment is zero and the substance is diamagnetic. However, if some half-filled orbitals are present the substance has net magnetic moment and is paramagnetic.