Question

$C{r}^{2+}$ is reducing in nature while the same $d-$orbital configuration $\left(d^4\right)M{n}^{+3}$ is an oxidising agent

Answer 1

If an element is behaving as reducing agent, that means, it itself is undergoing oxidation , that is , there is loss of electron. While for reduction there is gain of electron.
$C{r}^{2+}$ has the configuration $3d^4$. It can lose electron to form $3d^3$ which has stable configuration ( as it has half -filled $t_{2}g$ level). Hence , it is reducing.
On the other hand, $M{n}^{3+}$ also has $3d^4$. configuration but it can gain electron to form Mn²⁺ which has stable $3d^5$. configuration (as it is exactly half - filled). Hence oxidising.