Question

Following question is based on $Sc$ (Z$=$ 21) For 3d-electron, Z* is:

• A. $20.65$
• B. $16.85$
• C. $9.75$
• D. $3.00$

Answer 1

The correct option is D $3.00$

Sc $\left[Ar\right]3d^{1}4s^2$
Effective nuclear charge $Z_{eff}=Z-S$
where Z $=$ atomic number
and S $=$ screening constant
$=$ 0.35 per electron for electron in nth orbit.
$=$ 0.85 per electron for electrons in (n - 1)th orbit
$=$ 1.00 per electron for electrons in (n - 2)th, (n - 3)th, (n - 4)th orbit
$=$ 0.30 per electron in 1s-orbital (when alone)
This electron $3d^1$ is screened by 18 electrons of inner shell electrons.
Thus, $\sigma =\underset{\stackrel{}{8\times 1}}{(n-1)s^2{p}^6}+\underset{\stackrel{}{8\times 1}}{(n-2)s^2{p}^6}+\underset{\stackrel{}{2\times 1}}{(n-3)s^2}$
$=18$
Thus, $Z^{\ast }=21-18=3$