Given below are two statements :
Statement I : The first ionization enthalpy of Cr is lower than that of Mn.
Statement II : The second and third ionization enthalpies of Cr are higher than those of Mn. In the light of the above statements, choose the correct answer from the options given below :

We need to evaluate two statements about the ionization enthalpies of chromium (Cr, Z=24) and manganese (Mn, Z=25).

The electronic configurations are: Cr = [Ar] 3d$$^5$$ 4s$$^1$$ and Mn = [Ar] 3d$$^5$$ 4s$$^2$$.

Statement I: The first ionization enthalpy of Cr is lower than that of Mn.

For Cr, the first electron removed is the lone 4s$$^1$$ electron. For Mn, one of the paired 4s$$^2$$ electrons is removed. Although Mn has one more proton, Cr has a half-filled 4s subshell making removal relatively easier, while Mn has a fully filled 4s$$^2$$. The actual values are: IE$$_1$$(Cr) = 652.9 kJ/mol and IE$$_1$$(Mn) = 717.3 kJ/mol. So IE$$_1$$(Cr) < IE$$_1$$(Mn). Statement I is TRUE.

Statement II: The second and third ionization enthalpies of Cr are higher than those of Mn.

After losing one electron: Cr$$^+$$ = [Ar] 3d$$^5$$ (stable half-filled) and Mn$$^+$$ = [Ar] 3d$$^5$$ 4s$$^1$$.

The second ionization removes an electron from the very stable half-filled 3d$$^5$$ configuration in Cr$$^+$$, while for Mn$$^+$$ it removes the 4s$$^1$$ electron. So IE$$_2$$(Cr) > IE$$_2$$(Mn). This part is true.

After losing two electrons: Cr$$^{2+}$$ = [Ar] 3d$$^4$$ and Mn$$^{2+}$$ = [Ar] 3d$$^5$$ (half-filled, extra stable).

The third ionization removes from 3d$$^4$$ in Cr$$^{2+}$$ versus from the highly stable half-filled 3d$$^5$$ in Mn$$^{2+}$$. Therefore IE$$_3$$(Mn) > IE$$_3$$(Cr), meaning the third IE of Cr is lower than that of Mn.

Since the statement claims both second AND third IEs of Cr are higher than Mn, but only the second IE is higher (not the third), Statement II is FALSE.

Statement I is true and Statement II is false. The answer is Option C.