If M is the element of actinoid series, the degree of complex formation decrease in the order

Options

A. `M^(4+) gt M^(3+) gtMO_2^(2+) gt MO_2^(+)`
B. `MO_2^(+) gt MO_2^(2+) gt M^(3+) gt M^(4+)`
C. `M^(4+) gt MO_2^(2+) gt M^(3+) gt MO_2^(+)`
D. `MO_2^(2+) lt MO_2^(+) lt M^(3+) gt M^(3+)`

Explanation

To solve the question regarding the degree of complex formation of an element M from the actinoid series, we need to analyze the charges on the metal ions and their implications on complex formation.

### Step-by-Step Solution:

1. **Identify the Charges of Metal Ions**:
- The actinoid series includes elements that can exhibit multiple oxidation states. For element M, we consider the common oxidation states: M^4+, M^3+, Mo2^2+, and Mo2+.

2. **Understand the Relationship Between Charge and Size**:
- The degree of complex formation is influenced by the charge and size of the metal ion. Generally, a higher charge leads to a smaller ionic size, which enhances the ability to form complexes.

3. **Establish the Order of Complex Formation**:
- The order of complex formation is determined by the effective charge and size of the metal ions:
- M^4+ has the highest charge (+4), leading to a high degree of complex formation.
- Mo2^2+ has a charge of +6 (since it can be considered as M^6+), which is also significant, but the overall size might be larger compared to M^4+.
- M^3+ has a charge of +3, which is lower than M^4+ and Mo2^2+.
- Mo2+ has the lowest charge (+2), leading to the least degree of complex formation.

4. **Correct Order of Complex Formation**:
- Based on the analysis, the correct order of decreasing degree of complex formation is:
- M^4+ > Mo2^2+ > M^3+ > Mo2+

5. **Conclusion**:
- Therefore, the final answer to the question is that the degree of complex formation decreases in the order: M^4+ > Mo2^2+ > M^3+ > Mo2+.