Answer : The half-life of the radioactive isotope is, 200 min.
Solution :
As we know that the radioactive isotopes 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 = 600 min
a = initial amount of the reactant = 400 g
a - x = amount left after decay process = 50 g
Now put the all given 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 radioactive isotope is, 200 min.