Question

A sample originally contains 16 grams of a radioactive isotope. After 36 days, 14.8 grams of the isotope remain in the sample. What is the half-life of the isotope?

Enter your answer in the box. Round your answer to the nearest day.

Answer 1

The half-life is about 320 days

Explanation:

The fraction f remaining after d days is ...

f = (1/2)^(d/h) . . . . where h is the half-life

The value of h can be found from ...

log(f) = (d/h)·log(1/2) . . . . . take the log of both sides

h = d·log(1/2)/log(f) . . . . . . multiply by h/log(f)

h = 36·log(1/2)/log(14.8/16) ≈ 320 . . . . . fill in given values and evaluate

The half-life is about 320 days.