The half-life of a radioactive substance is 14 days. After 7 days a sample of the substance has been reduced to a mass of 7 mg. What is the initial mass? When will there only be 0.2 left?

Answer 1

This is an example of exponential decay.

m(t) = m₀ (0.5)^t/T

m₀ = initial amount in mg

T = half-life in days = 14

t = time elapsed in days from when m was m₀

7 = m₀ (0.5)^7/14 = m₀ (0.5)^1/2

m₀ = 7 / (0.5)^1/2 mg = 9.9 mg

m(t) = 9.9 (0.5)^t/14 (in mg)

For the second question, set

0.2 = 9.9 (0.5)^t/14

and solve for t. Start by taking the log of both sides. Can you finish from here?