What are 'energy levels'? Explain the arrangement and distribution of electrons in the various shells with reference to an atom in general and to an atom of potassium $^{39}_{19}\text{K}$ with special reference to the 2n² rule.

Electrons revolve around the nucleus in fixed orbits. Each orbit is associated with a certain amount of energy hence named 'energy levels'.

Arrangement of electrons :

• The shell closest to the nucleus is called K shell [first shell or number one shell].
• The next shell is called the L shell [second shell or number 2 shell]
• Following shells are M,N…etc.
• An electron has minimum energy in the first or K shell and the energy increase in the order K, L, M, N.
• The maximum number of electrons which can be present in any shell of an atom is given by or represented by a formula 2n², where n is equal to the number of the shell as counted from the nucleus.

• The outer most shell cannot have more than 8 electrons.
• The penultimate shell [last but one ] cannot have more than 18 electrons.
• A new shell is formed as soon as the - outermost shell attains 8 electrons.

With reference to Potassium $^{39}_{19}\bold{K}$ :

    No. of Electrons [e] = 19
    No. of Protons [p] = 19
    No. of Neutrons [n] = A - Z
    = 39 - 19 = 20

The two rules governing the distribution of electrons are:

1. Rule 1 — Maximum number of electrons in each shell is given by the formula 2n²
2. Rule 2 — The outermost shell cannot have more than 8 electrons.

As per rule 1 (2n² rule), distribution of electrons for Potassium will be:

But as per rule 2, outermost shell cannot have more than 8 electrons. So M shell will have 8 electrons and a new shell (N) will be formed with 1 electron. Hence, the final electronic configuration of Potassium will be:

∴ Electronic configuration of Potassium = 2, 8, 8, 1