Question

Calculate the shielding effect and the effective nuclear charge of $F{e^{2 + }}$ ion.

Answer 1

Hint : The effective nuclear charge is the net force experienced by an electron in a valence shell whereas the shielding effect explains the drag of the protons on the electrons present in the valence shell and the repulsive forces acting between valence shell electrons and electrons present in inner orbitals.

Complete Step By Step Answer:
Screening constant is the summation of the values calculated as per following rules:
The other electron which is present in the same shell as the electron under observation, will provide a shielding effect to the extent of $0.35$ nuclear charge with an exception of electrons present in $1s$ shell which contribute a value of $0.30$ for each electron.
The electrons present in the $n - 1$ shell contribute a value of $0.85$ per electron.
The electrons present in the $n - 2$ shell then will contribute a value of $1.0$ per electron.
If the electrons are present in d-orbital or f-orbital, then the contribution of electrons in the orbitals other than d-orbital or f-orbital will be $1.0$ per electron.
To calculate the shielding effect or screening constant of the given ion, we need to follow some steps which are as follows:
Step-1: Write complete electronic configuration of the given ion.
Given ion $= F{e^{ + 2}}$
Atomic number of iron metal $= 26$
Number of electrons present in $F{e^{2 + }}$ ion $= 24$
Therefore, electronic configuration of $F{e^{2 + }}$ ion $= 1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}3{d^6}$
Step-2: As per rules, calculating the value of screening constant.
$S = 0.35 \times 5 + 1 \times 18$
$\therefore S = 19.75$
Now, the effective nuclear charge is related to the screening constant as follows:
${Z_{eff}} = Z - S$
Where, ${Z_{eff}} \Rightarrow$ effective nuclear charge
$Z \Rightarrow$ Atomic number
$S \Rightarrow$ Screening constant
Substituting values to calculate the effective nuclear charge of $F{e^{2 + }}$ ion:
${Z_{eff}} = 26 - 19.75$
$\therefore {Z_{eff}} = 6.25$
Hence, the shielding effect and the effective nuclear charge of $F{e^{2 + }}$ ions is $19.75$ and $6.25$ respectively.

Note :
The value of screening constant differs according to the position of the electron. If the position of the electron is specified in the question, then calculate the screening constant accordingly but if it is not mentioned then by default, you have to calculate the screening constant for electrons present in the valence subshell.