a
The order can be explained using the idea of spin correlation. Spin correlation refers to lowering of energy for like (parallel) spins. Spin correlation leading to decrease in repulsion for electrons of like spins than for electrons of different spins is called exchange energy.

Spin correlation and its exchange energy gives an electronic configuration a special stability which is greatest for half Filled electronic configurations. \(\mathrm{Mn}^{2+}\left(\mathrm{d}^{5}\right)\) gets stabilisation due to half-filled configuration.

In \(Fe^{2+}\left(d^{6}\right)\) the placing of one extra electron in a subshell destabilises. Placing of \(2\) electrons in \(\mathrm{Co}^{2+}\left(\mathrm{d}^{7}\right)\) destabilises it more. \(\mathrm{Cr}^{2+}\left(\mathrm{d}^{4}\right)\) has one vacant subshell. Fe \(^{2+}\) gets more stabilisation compared to \(\mathrm{Cr}^{2+}\) through exchange energy. So the order is as follows:

\(\mathrm{Mn} > \mathrm{Fe} > \mathrm{Cr} > \mathrm{Co}\)