At this time, we have 1.0mg of 137Cs; after 30 years, we shall have one half of the original, or 0.50mg; after 60 years, we shall have 0.25mg; after 90 years, we shall have 0.125mg and , finally after 120 years, we shall have 0.0625mg.
After 30 years − 0.50mg
60 years − 0.25mg
90 years − 0.125mg
120 years − 0.0625mg
Alternative solution: Total time =120 years
We know that, total time =n×t1/2
So, 120=n×30
n=4
Thus, the quantity of the isotope left after four half life periods =(12)4N0=(12)4×1
=16=0.0625mg