What is the half-life period of a radioactive material if its activity drops to 1/16^th of its initial value in 30 years ?

Explanation:

Radioactive decay follows an exponential pattern, where the quantity of a substance reduces by half over each half-life period.

If a substance's activity drops to 1/16 of its original value, it implies that four half-lives have elapsed, because:

(1/2)⁴ = 1/16

Step-by-Step Calculation:

Given that four half-lives correspond to 30 years, the duration of one half-life can be calculated as:

Half-life = Total time / Number of half-lives

Substituting the values:

Half-life = 30 years / 4 = 7.5 years

Final Answer

The half-life period of the radioactive material is 7.5 years.