Question

Why are the electronic configuration numbers the way they are? $\left(2,8,18,32,\dots \right)$ How were they determined?

Answer 1

Quantum Number:

• Each atom's electron is given one of four quantum numbers, the primary quantum number (symbolized $\mathrm{n}$), to characterize the state of that electron. It is a discrete variable since the values are all-natural integers starting at $1$.
• The azimuthal quantum number$\text{l}$, the magnetic quantum number ${\mathrm{m}}_{\mathrm{l}}$, and the spin quantum number $\mathrm{s}$ are the additional quantum numbers for bound electrons in addition to the primary quantum number.
• According to Niels Bohr, electrons will fill up the shells in accordance with the primary quantum number.

Electronic Configuration:

• Based on the primary quantum number, the maximum number of electrons that can fit in a shell may be calculated (n).
• The formula for it is $2{\mathrm{n}}^2$, where n is the shell number.
• The table below lists the shells, $\mathrm{n}$ values, and the total number of electrons that can fit.

Shell and ‘n’ value	Maximum electrons present in the shell
K shell, $\mathrm{n}=1$	$2\times {\left(1\right)}^2=2$
L shell, $\mathrm{n}=2$	$2\times {\left(2\right)}^2=8$
M shell, $\mathrm{n}=3$	$2\times {\left(3\right)}^2=18$
N shell, $\mathrm{n}=4$	$2\times {\left(4\right)}^2=32$

• It is used to forecast how many electrons will be in each shell.
• Its electrical configuration will be $2,8,1$ in accordance with this guideline.
• The greatest number of electrons that can enter the final shell, where there is just one, is $18$.