Question

A sample of 4 g of cobalt isotope is produced. If the half-life of is 30 years, what will be the mass of the cobalt remaining after 90 years?

Answer 1

Answer:

1/2 gram.

Explanation:

There are $90/30 = 3$ half-lives in that 90 years. The mass of this sample will have became $(1/2)^{3} = 1/8$ that of the original value by then. That is:

$\displaystyle m(90\;\text{years}) = \left(\frac{1}{2}\right)^{90/30}\cdot m_0 = \frac{1}{8}\times 4 = \rm \frac{1}{2}\; g$.

Answer 2

A sample of 4 g of cobalt isotope is produced. If the half-life of is 30 years, what will be the mass of the cobalt remaining after 90 years is 0.5 g.

Explanation:

After 30 years the amount of cobalt isotope will be half of the original value, which is 2 g. After 60 years means, this will be decremented half of that 2 g  which is 1 g. After 90 years, it will be half of the previous value that will be equal to 0.5 g.

(i.e) $4 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = 0.5 g$