Question

Element X is a radioactive isotopes such that every 24 years, it’s mass decreases by half. Given that the initial mass of a sample of element X is 70 g, how long would it be until the mass of the sample reach 61 g, to the nearest 10th of the year?

Answer 1

t=4.8

Explanation:

We get to use the simple version of the half-life equation: where N is the amount of radioactive element left after a specific number of years, N0 is the initial amount of the element, t is the number of years (our unknown), and H is the Half-life of the element. For us, N is 61 N0 is 70, t is unknown, and H is 24 years. We begin by dividing both sides by 70 and then take the natural log of both sides which allows us to bring down the exponent to the front on the right side. We divide both sides by ln(.5) and then multiply both sides by 24 to get: t = 4.8 years