Chromium-51 has a half-life of 28 days. You have a sample of chromium-51 that weighs 100 grams. How long will it take for the sample to decay to a mass of 5 grams?

Question

I looked it up online, and used the equations listed; Initial amount x e^kt=m where k is equal to (ln2)/half life, but got a negative answer. I also feel like there should be a way to write it as a simpler exponential/log equation, like a reverse of compound interest

Answer 1

Let A(t) = amount remaining after t days.

A(t) = 100e^kt

50 = 100e^28k

So, e^28k = 0.5

28k = ln(0.5)

k = -0.024755

A(t) = 100e^-0.024755t

Find t so that A(t) = 5:

5 = 100e^-0.024755t

0.05 = e^-0.024755t

ln(0,05) = -0.024755t

So, t ≈ 121 days.

Answer 2

See the video.