Question

A radioactive isotope has a half-life of days, and a sample of this isotope has a mass of mg initially. When will there be only 8mg remaining? (Round your answer to the nearest day.)

Answer 1

Answer:

11 days.

Explanation:

According to the statement, the radioactive isotope has a half-life greater than 1 day and lesser than 7 days. Let assume that the radioactive isotope has a half-life of 4 days and the initial mass is 50 mg. The time constant is:

$\tau = \frac{4\,days}{\ln 2}$

$\tau = 5.771\,days$

The time when mass is reduced to 8 milligrams is:

$t=-(5.771\,days)\cdot \ln\frac{8\,mg}{50\,mg}$

$t \approx 10.576\,days$

It is approximately 11 days.