Step 1: Understanding the Question:
The question relates to the size trend of actinide ions in their trivalent state (+3).
Step 2: Detailed Explanation:
1. In the actinide series, as we move from left to right (increasing atomic number), there is a steady decrease in the size of the atoms and ions ($M^{3+}$). This phenomenon is known as "actinide contraction".
2. The contraction occurs because of poor shielding of the nuclear charge by the 5f electrons.
3. Let's look at the atomic numbers of the given elements:
- Uranium (U): $Z = 92$
- Berkelium (Bk): $Z = 97$
- Einsteinium (Es): $Z = 99$
- Mendelevium (Md): $Z = 101$
4. Since Uranium has the lowest atomic number among the options, it is the first to appear in the series. Therefore, $U^{3+}$ will have the largest ionic radius.
Step 4: Final Answer:
Uranium in its +3 state has the largest size among the given options.