Question

which radioactive sample would contain the greatest remaining mass of radioactive isotope after 10 years

Answer 1

The radioactive sample with the greatest remaining mass after 10 years is 4.0 grams of
`\(^(60)\text{Co}\)` (Option D).

The rate of radioactive decay is characterized by the half-life of each isotope. The longer the half-life, the slower the decay rate. In this case:

A.
`\(^(198)\text{Au}\)` has a half-life of 2.7 days.

B.
`\(^(42)\text{K}\)` has a half-life of 12.4 hours.

C.
`\(^(32)\text{P}\)` has a half-life of 14.3 days.

D.
`\(^(60)\text{Co}\)` has a half-life of 5.3 years.

After 10 years,
`\(^(198)\text{Au}\), \(^(42)\text{K}\), and \(^(32)\text{P}\)` would have undergone substantial decay, but
`\(^(60)\text{Co}\)` would remain relatively unchanged due to its longer half-life. Therefore, the sample with the greatest remaining mass after 10 years would be D, 4.0 grams of
`\(^(60)\text{Co}\).`

The probable question may be:

Which radioactive sample would contain the greatest remaining mass of the radioactive isotope after 10 years?

A. 2.0 grams of 198 Au

B. 2.0 grams of 42 K

C. 4.0 grams of 32 P

D. 4.0 grams of 60 Co