If the fraction of the atoms of a radioactive material left after 120 years is 1/64, what is the half-life of the material?

If the fraction of the atoms of a radioactive material left after 120 years is 1/64, what is the half-life of the material?

Answer Details

Given amount remaining = 164 $\frac{1}{64}$

= 164=1(2)6 $\frac{1}{64}=\frac{1}{(2{)}^6}$

∴ $\therefore$ = 120years6 $\frac{120\text{years}}{6}$ = 20 years

⇒ $\Rightarrow$ T12 $\frac{1}{2}$ = 20 years