Seven-eighths of a sample of hydrogen-3 will have become a stable isotope after 36.9 years. what is the half-life of hydrogen-3? 12.3 years 18.5 years 32.3 years 36.9 years

12.3 years

Explanation:

The equation of the radioactive decay can be written as follows:

(1)

where

N(t) is the amount of radioactive sample left at time t

N0 is the amount of radioactive sample at time t=0

t is the time passed

is the half-life of the isotope

The problem tells us that after t=36.9 y, the amount of sample which has become stable is 7/8. This means that 7/8 of the sample has already decayed, so the amount of radioactive sample left is

We can now re-arrange equation (1) by using this information and by substituting t=36.9 y we find:

So, the answer is

12.3 years