Question

Calculate the effective nuclear charge experienced by the $4s$ electron in potassium atom($Z=19$.

Answer 1

Hint: The effective nuclear charge is the true nuclear charge minus the screening constant. It is due to the valence electrons present in the atom. The effective nuclear charge will be according to the formula and consequently, the effective nuclear charge will be the difference between the true nuclear charge and the screening constant.

Complete step by step answer:
We know that the effective charge is the true nuclear charge minus the screening constant. It is due to the valence electrons present in the atom. We have been given the potassium atom with the atomic number nineteen.
The electronic configuration of potassium, K is as follows
$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^1$
Here it is having four shells in it. Therefore the formula for the effective nuclear charge is as follows
$(Z_{eff}{)}_{4s}=Z-\sigma$
Where $Z_{eff}$ is the effective nuclear charge
$\sigma$ is the screening constant
$\sigma =$ $0.85\times$number of electrons in $(n-1)$ the shell $+1.00$ $\times$ total number of electrons in the inner shell
$\Rightarrow 0.85\times 8+1.00\times 10$
$\Rightarrow 16.80$
Hence, $Z_{eff}=Z-\sigma$
$\Rightarrow 19-16.80$
$\Rightarrow 2.20$
Where the number of electrons in $(n-1)$ th shell is eight
Total number of electrons in the inner shell is ten
Hence the effective nuclear charge of the potassium is $2.20$

Note: Effective nuclear charge increases from left to right across the row of a periodic table. It shows a sudden decrease when we go from one end of one row to the beginning of the next row in the periodic table. Also, the change in effective nuclear charge going down a column of the periodic table is generally less than that going across a row of the periodic table.
The rule used in finding the screening constant is termed to be Slater’s rule.