Explain briefly how the $+2$ oxidation state becomes more stable in the first half of the first-row transition elements as the atomic number increases.

(N/A) The $+2$ oxidation state is achieved by the loss of two $4s$ electrons from the metal atoms. As we move from $Sc$ $(Z=21)$ to $Mn$ $(Z=25)$,the number of electrons in the $3d$ orbital increases from $1$ to $5$. The electronic configurations for the $+2$ ions are as follows:
$Sc^{2+}: 3d^1$
$Ti^{2+}: 3d^2$
$V^{2+}: 3d^3$
$Cr^{2+}: 3d^4$
$Mn^{2+}: 3d^5$
As the number of $d$ electrons increases,the $d$-orbital approaches a half-filled configuration. According to Hund's rule and the principle of exchange energy,a half-filled $d^5$ configuration is exceptionally stable. Therefore,the stability of the $+2$ oxidation state increases across the series,reaching a maximum stability at $Mn^{2+}$ due to its stable $d^5$ configuration.