Question

Why are electronic configuration numbers the way they are ? $2,8,18,32$ …. So on and how are they determined.

Answer 1

Electronic configuration is the systematic method of arranging electrons in the various orbitals and energy levels in an atom. The electronic configuration numbers simply indicated the maximum number of electrons that can be contained in each shell.

Complete answer:
The structure of an atom is such that the electrons are placed in energy levels called shells in an increasing order and these shells are located outside the nucleus which contains the protons and neutrons.
Each shell or energy level can accommodate a fixed number of maximum electrons beyond which the electrons start filling up the next shell. These numbers are called the electronic configuration numbers are represented as: $2,8,18,32$ ……
The maximum number of electrons that a shell can accommodate is determined using the following formula:
$\max {\text{ electrons in a shell(n)}} = 2 \times {(n)^2}$ where the value of shell number $n$ can be any natural number.
For example, the first four shells can be represented as follows:
$\max {\text{ electrons in a shell(1)}} = 2 \times {(1)^2} = 2$
$\max {\text{ electrons in a shell(2)}} = 2 \times {(2)^2} = 8$
$\max {\text{ electrons in a shell(3)}} = 2 \times {(3)^2} = 18$
$\max {\text{ electrons in a shell(4)}} = 2 \times {(4)^2} = 32$
The formula is based on the fact that each orbital in a subshell can contain a maximum of two electrons and the squares of the energy levels gives us the total number of subshells that a shell contains.
For example, the first energy level only contains the s-subshell that has a single orbital that can accommodate two electrons only. The second shell contains the s-subshell as well as the p-subshell. The s-subshell contains only one orbital and two electrons, the p-subshell contains three orbitals and a maximum of six electrons thus allowing a total of eight electrons in the second shell.
$n = 1 \Rightarrow s(2{\text{ electrons)}}$
$n = 2 \Rightarrow s(2{\text{ electrons)}} + p(6{\text{ electrons) = 8}}$
$n = 3 \Rightarrow s(2{\text{ electrons)}} + p(6{\text{ electrons)}} + d(10{\text{ electrons)}} = 18$
$\Rightarrow$ Hence the electronic configuration numbers are like $2,8,18,32$ and so on.

Note:
The electronic configuration numbers indicate the maximum capacity of accommodating electrons in a shell, but it does not mean that each shell always contains a fixed number of electrons in it. The shells and orbitals can be partially or completely filled.