A pure radioactive substance has a mass of 30 micrograms but had a mass of 240 micrograms 48 years ago.Assuming that the only changes in mass are due to radioactive decay, the half-life of the substance is _______ years.

Question

Quizplus · Accepted Answer

The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the substance has lost 240 - 30 = 210 micrograms of mass over a period of 48 years.

Using the formula for radioactive decay, we can find the number of half-lives that have occurred:

N = N0 (1/2)^(t/T)

Where N is the current mass, N0 is the original mass, t is the time elapsed, T is the half-life.

Plugging in the given values gives:

30 = 240 (1/2)^(48/T)

Simplifying:

1/8 = (1/2)^(48/T)

Taking the logarithm of both sides:

-3 = 48/T * log(1/2)

Solving for T:

T = 16 years.

Therefore, the answer is D.

A Pure Radioactive Substance Has a Mass of 30 Micrograms