Explain the variations in atomic radii of transition elements along the period. The following table provides data for the first transition series:

Element	Sc	Ti	$V$	Cr	Mn	Fe	Co	Ni	Cu	Zn
Metallic Radius $M$ (pm)	$164$	$147$	$135$	$129$	$137$	$126$	$125$	$125$	$128$	$137$

(N/A) The atomic radii of transition elements in a period generally decrease with an increase in atomic number, but this decrease becomes small after the middle of the series.
$1$. In the beginning of the series, the atomic radii decrease as the atomic number increases due to the increase in effective nuclear charge. The attraction between the nucleus and the outermost electrons $(4s)$ increases, resulting in a decrease in atomic radii from $Sc$ to $Cr$.
$2$. In the middle of the series, the shielding effect of $d$-electrons and the increasing nuclear attraction are counterbalanced. As a result, the atomic radii remain almost steady from $Cr$ to $Cu$.
$3$. At the end of the series, the electron-electron repulsions in $d$-orbitals become dominant over the nuclear attraction. These repulsions expand the electron cloud, which results in an increase in atomic radii. For example, the atomic radius of $Zn$ $(137 \text{ pm})$ is greater than that of $Cu$ $(128 \text{ pm})$.