Question

For $Cu$, effective nuclear charge felt by a $4s$-electron is:

• A. $2.2$
• B. $2.95$
• C. $1.0$
• D. $1.65$

Answer 1

Answer: (A)

$2.2$

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 is screened by 18 electrons in (n - 1), 8-electrons in (n - 2) and 2-electrons in (n-3)
Thus, $\sigma =\underset{\stackrel{}{8\times 0.85}}{(n-1)s^2{p}^6}+\underset{\stackrel{}{1\times 10}}{(n-1)d^{10}}+\underset{\stackrel{}{8\times 1}}{(n-2)s^2{p}^6}+\underset{\stackrel{}{2\times 1}}{(n-3)s^2}$
$=26.8$
Thus, $Z^{\ast }=29-26.8=2.2$