Explain the rule with example according to which electrons are filled in various energy levels.

Neil Bohr and Charles Bury proposed a scheme for distribution of electrons in different shells of an atom based on the formula 2n², where n denotes the number of shell.

The following rules are followed for writing the number of electrons in different energy levels or shells:

1. The maximum number of electrons in each shell or orbit is determined by the formula 2n², where n is the number of shell.
   K shell, n=1, no. of electrons = 2 x 1² = 2
   L shell, n=2, no. of electrons = 2 x 2² = 8
   M shell, n=3, no. of electrons = 2 x 3² = 18
2. Electrons are not accommodated in a given shell, unless the inner shells are filled. Shells are filled in step-wise manner.
3. The atom's outermost shell needs 2 electrons for stability (duplet rule) if it has only one shell. If it has multiple shells, it requires 8 electrons (octet rule) in the outermost shell for stability.

Example: Potassium has 19 electrons. The first shell will take 2 electrons, second shell will take 8 electrons. Remaining 9 electrons should be taken by third shell but according to octet rule, the outermost shell should not accommodate more than 8 electrons. So third shell take 8 electrons and remaining 1 electron will go to fourth shell. So electronic configuration of potassium is:

$\begin{matrix} \text{K} & \text{L} & \text{M} & \text{N} \\ 2 & 8 & 8 & 1 \end{matrix}$