Answer : The correct option is, (2) 3.82 d
Solution : Given,
As we know that the radioactive decays follow first order kinetics.
So, the expression for rate law for first order kinetics is given by :
where,
k = rate constant
t = time taken for decay process = 11.46 days
a = initial amount of the reactant = 200 g
a - x = amount left after decay process = 25 g
Putting values in above equation, we get the value of rate constant.
Now we have to calculate the half life of a radioisotope.
Formula used : 
Putting value of 'k' in this formula, we get the half life.

Therefore, the half-life of a radioisotope is, 3.820 d