Calculate the $Z_{eff}$ on the electron present in $5 d -$ orbital of $G d$ (Atomic number $= 64$ ).

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Solution

Electronic configuration of $G d$ is
$1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 4 f^{7}$
$5 s^{2} 5 p^{6} 5 d^{1} 6 s^{2}$
For d electrons,
screening constant = 61 (ns, np and (n -1) electrons contribute 1 to the shielding effect)
$Z_{e f f e c t i v e} = 64 - 61 = 3$

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