The half-life of hydrogen-3 is 12.32 years. If a sample has a mass of 700 mg, find the mass (in mg) that remains after 20 years.

Answer 1

Amount, A=A₀(e)^kt , where A₀ = original amount

ln(1/2) = k(12.32)

k = ln(1/2)/12.32

A(t) = A₀e^{ln(1/2)t/12.32} = A₀(1/2)^t/12.32 = A₀(2)^-t/12.32

A(20) = 700(2)^-20/12.32 = 700(0.32457) =227.20 grams

Checking:

t A

0 700

12.32 350

24.64 175

So between 350 and 175, 227.20 makes sense.