Step 1: Understand the format.
We check both statements for truth and then see if the Reason explains the Assertion.
Step 2: Check the Assertion.
Actinoids do show a wide range of oxidation states because the 5f, 6d and 7s orbitals are close in energy, so many electrons can take part in bonding. So the Assertion is TRUE.
Step 3: Check the Reason.
Actinoids are indeed radioactive in nature. So the Reason is also TRUE.
Step 4: Test the explanation link.
The wide range of oxidation states comes from the closeness in energy of the 5f, 6d and 7s orbitals, not from radioactivity. Radioactivity is a separate property. So the Reason does NOT explain the Assertion.
Step 5: Conclude.
Both A and R are true but R is not the correct explanation of A, which is option 2.
\[ \boxed{\text{Both A and R true; R is not the correct explanation}} \]