Question

Calculation of effective nuclear charge on 4s and 3d electron in scandium atom

Answer 1

Solution is in the pic .... :)

Answer 2

Answer:  

The effective ‘nuclear charge’ for 4s and 3d electrons in Sc is 1.65 and 3 respectively.

Solution:

The ‘electronic configuration’ of Sc by Aufbau principle is $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{1}$.

The effective ‘nuclear charge’ is found by using the following formula

$Z^{*}=Z-\sigma$

Here, $Z^{*}$ is the ‘effective nuclear’ charge and Z is the atomic number and σ is the shielding factor.

The shielding factor can be determined by arranging the electronic configuration according to slater’s rule.

The slater’s rule state that the electronic configuration should be written in the increasing order of principle quantum number “n” and then the s and p orbitals should be written in a group.  

So the electronic configuration of Sc according to Slater’s rule will be written as $\bold{\left(1 s^{2}\right)\left(2 s^{2} 2 p^{6}\right)\left(3 s^{2} 3 p^{6}\right)\left(3 d^{1}\right)\left(4 s^{2}\right).}$

Then we have to decide effective nuclear charge is required for which electron. So we have to multiply the remaining ‘electrons’ in the same group with 0.35 and the number of electrons in other lower groups should be multiplied with 1. The sum of both the numbers will give the shielding effect. In this case, if we first require to find the nuclear shielding factor for 4s electrons, then it will be like

$\sigma=(1 \times 0.35)+(19 \times 1)=19.35$

The value 1 in the first term is denoted to the remaining one electron in the 4s shell and the value 19 in the second term is denoted to the remaining electrons in the lower shells.

Thus the effective nuclear charge for 4s electrons in Sc is  

$Z^{*}=21-19.35=1.65$

Similarly for 3d electron, the shielding factor is  

$\sigma=(0 \times 0.35)+(18 \times 1)=18$

The value 0 in the first term is denoted to the remaining one electron in the 3d shell and the value 18 in the second term is denoted to the remaining electrons in the lower shells.

Thus the effective nuclear charge for 3d electrons in Sc is  

$Z^{*}=21-18=3$

Thus, the effective nuclear charge for 4s and 3d electrons in Sc is 1.65 and 3 respectively.