Question

How would you find the quantum numbers for an atom?

Answer 1

Hint: The answer is based on the concept of the four quantum numbers assigned for each atom that are the principal, azimutal, magnetic and spin quantum numbers and assign the numbers as per these theories.

Complete step – by – step answer:
In the lower classes of general chemistry, we have studied the basic concept of the four types of quantum numbers and also to assign those quantum numbers to the atoms individually.
Let us now see in detail about these quantum numbers and obtain the required answer based on their definitions.
- There are a total of four quantum numbers and we shall see this in detail.
1) Principal quantum number: This is denoted by the letter $n$ and has the integral values 1,2,3…. This number determines the size and the energy of the orbital.
2) Angular quantum number also called as the Azimuthal quantum number: This is denoted by the letter$l$ and is associated with the number of different subshells in an energy level that is the values will be 0,1,2,3,…………(n-1)
3) Magnetic quantum number: This is denoted by the letter ${{m}_{l}}$ and it describes the orientation of each orbital in space and this number can have the integral values from $-l$to$+l$
4) Spin quantum number: This is denoted by ${{m}_{s}}$ and this describes the direction of the spin of the electrons and the values for this are only two that is $+\dfrac{1}{2}$ and $-\dfrac{1}{2}$
Let us consider an example of sodium with atomic number 11 and the electronic configuration $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{1}}$
Here, 3s is the outermost shell and therefore the principal quantum number will be $n=3$
There is only one subshell that is the' subshell and thus the Azimuthal quantum number will be $l=0$
Since there is only one possible orbital, the magnetic quantum number will be ${{m}_{l}}=0$
Also, the spin quantum number can be $s=+\dfrac{1}{2}or-\dfrac{1}{2}$

Note: Note that no two electrons in an atom can have identical sets of all the quantum numbers that is in simple words no two electrons in an atom can have all the quantum numbers same. This principle is known as the Pauli’s exclusion principle.