Please help me with this Chemistry question.

Question

A 5.0 gram sample of a radioactive element was formed in a 1960 explosion of an atomic bomb at Johnson Island in the Pacific test site. The half-life of the radioactive element is 28 years. How much of the original sample will remain in the year 2025? Show your work for credit.

Answer 1

There are a couple of ways to answer this type of question. I find the easiest is to use the formula

FR = 0.5ⁿ

FR = fraction remaining = ?

n = number of half lives that have elapsed = see below

years elapsed = 2025 - 1960 = 65 years

number of half lives elapsed = n = 65 yrs / 28 yrs = 2.32 half lives

FR = 0.5^2.32 = 0.196

amount remaining = 5.0 g x 0.196 = 0.98 g remain