Question

Element X is a radioactive isotope such that every 14 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 360 grams, how long would it be until the mass of the sample reached 100 grams, to the nearest tenth of a year?

Answer 1

25.9 years

Explanation:

The half life of an isotope is related to the actual amounts by the equation:

N = Ni*(1/2)^(t/HL)

where N and Ni are the final and initial (Ni) amounts, t is the time (in years for this problem) and HL is the half-life, in years.

In this problem, we can write:

100 = 360*(1/2)^(x/14)

I'll reduce this to:

1 = 3.6*(1/2)^(x/14)

This can be solved by taking the log of both sides.

x = 25.87 or 25.9 years