Given, rate constant (k)=0.05μg/ year
Thus, from the unit of k, it is clear that the reaction is zero order. Now, we know that
half-life (t1/2​) for zero order reaction =2ka0​​
where, a0​= initial concentration,
k= rate constant
t1/2​=2×0.05μg/ year 5μg​
=50 years
Thus, 50 years are required for the decomposition of 5μg of X into 2.5μg.