If a sample of a radioactive isotope decays from 400 grams to 50 grams in 6 days, find the half-life of the isotope. Simplify your answer as much as possible.

Answer 1

50 = 400e^6k

0.125 = e^6k

ln 0.125 = 6k

-2.07944 ≈ 6k

-0.34657 ≈ k

0.5 = e^-0.34657t

ln 0.5 = -0.34657t

-0.6931 ≈ -0.3457t

2.0051 ≈ t

Answer 2

After every half life, mass is halved

So after 1 half life we have 200g, after 2 half lives 100g, after 3 half lives 50g

So 3 half lives = 6 days

So 1 half life = 2 days.