The electronic configuration of an element describes how electrons are distributed in its atomic orbitals. Potassium (K) has an atomic number of 19, meaning it has 19 electrons to place in orbitals following the Aufbau principle, Pauli exclusion principle, and Hund's rule. The order of filling is based on increasing energy levels: 1s, 2s, 2p, 3s, 3p, 4s, 3d, etc.

Step 1: Fill the 1s orbital with 2 electrons: $1^{2}$

Step 2: Fill the 2s orbital with 2 electrons: $2^{2}$

Step 3: Fill the 2p orbital with 6 electrons: $2^{6}$

Step 4: Fill the 3s orbital with 2 electrons: $3^{2}$

Step 5: Fill the 3p orbital with 6 electrons: $3^{6}$

Step 6: The next orbital is 4s, which has lower energy than 3d. Place the remaining 1 electron in 4s: $4^{1}$

Thus, the shell-wise (principal quantum number n) electronic configuration for potassium is written by grouping electrons with the same n:

$K (19) : n = 1 : 2, n = 2 : 8, n = 3 : 8, n = 4 : 1$

This means the first shell (n=1) has 2 electrons, the second shell (n=2) has 8 electrons, the third shell (n=3) has 8 electrons, and the fourth shell (n=4) has 1 electron.

Related Topics

Electronic Configuration: The arrangement of electrons in an atom's orbitals, following specific rules to achieve the lowest energy state.

Shells and Subshells: Electrons occupy shells (n=1,2,3,...), which contain subshells (s, p, d, f). Each subshell has orbitals that hold a maximum of 2 electrons.

Formulae

Maximum electrons in a shell: $2 n^{2}$ , where n is the principal quantum number.

For potassium (n=4 shell), maximum electrons possible is $2 \times 4^{2} = 32$ , but only 1 electron is present in n=4.