Question

The ${}^{60}Co$ isotope decays with a half life of $5.3$ years. How long would it take for $7/8$ of a sample of $500$ $mg$ of ${}^{60}Co$ to disintegrate?

• A. $21.2$ years
• B. $15.9$ years
• C. $10.6$ years
• D. $5.3$ years

Answer 1

The correct option is B $15.9$ years

After disintegration of 7/8 of a sample, the remaining will be 1/8 of the initial value.

Time taken to become ${\left(\frac{1}{2}\right)}^3$ of initial $\Rightarrow$ 3 half lives

Half life of ${60}_{Co}$ isotope = 5.3 years

$\therefore$Total time taken for disintegration of 7/8 of a sample of 500mg of ${60}_{Co}$ is 15.9 years.