Look at their electronic configurations.
Cr: [Ar] 3d5, 4s1
Mn: [Ar] 3d5, 4s2
Cr only has one electron in the orbital that is 4s, whereas Mn has two. The two electrons in Mn's 4s orbital repell each other, so one is more easily removed than in Cr. Answer A is kind of an oversimplification, though it does imply this.
becoz it is difficult to remove an electron from the half filled(symmetrical) d orbital. so chromium has more ionisation energy than manganese which has unsymmetric d- orbitoal
The 1st ionization energy for Cr is less than that of Mn. The latter can be explained as follow: Consider the electron configuration for manganese,
Mn: [Ar] 3d54s2 vs. Cr: [Ar] 3d54s1. It is more difficult to remove an electron from 4s2 orbital because the orbital is full, and would require a large amount of energy to removed one electron from a set of paired electrons in 4s2. Also, s- electrons are extremely good at penetrating the inner electron cloud in order to feel the nuclear charge, so it would be held more tightly by the nucleus, which contributes to the stability of atom. Also, electron- electron repulsions in s- orbitals seem to be less important as opposed to those paired in p or d orbitals. Perhaps, it is related to the spherical shape of the s orbital.