Which transition element ion M^+3 has electronic configuration 3d^54s…

The correct answer is Option (3) → $Fe^{3+}$.

To determine which transition metal corresponds to the given electronic configuration, we start by analyzing the electron configurations of the transition metals and their oxidation states:

1. Chromium (Cr):

Atomic number = 24

Ground state electronic configuration: \( [Ar] 3d^5 4s^1 \)

For \( \text{Cr}^{3+} \), we remove one 4s electron and two 3d electrons: 

\([Ar] 3d^3 4s^0\)

2. Manganese (Mn):

Atomic number = 25

Ground state electronic configuration: \( [Ar] 3d^5 4s^2 \)

For \( \text{Mn}^{3+} \), you remove two 4s electrons and one 3d electron: 

\([Ar] 3d^4 4s^0\)

3. Iron (Fe):

Atomic number = 26

Ground state electronic configuration: \( [Ar] 3d^6 4s^2 \)

For \( \text{Fe}^{3+} \), you remove two 4s electrons and one 3d electron: 

\([Ar] 3d^5 4s^0\)

4. Cobalt (Co):

Atomic number = 27

Ground state electronic configuration: \( [Ar] 3d^7 4s^2 \)

For \( \text{Co}^{3+} \), you remove two 4s electrons and one 3d electron: 

\([Ar] 3d^6 4s^0\)

Conclusion:
The correct transition element ion \( \text{M}^{3+} \) with the electronic configuration \( 3d^5 4s^0 \) corresponds to iron (Fe). Thus, the answer is \(Fe^{3+}\).