The half-life of hydrogen-3 (tritium) is approximately 12 years. In how many years will half of a 20-gram sample decay by beta radiation to helium-3?

6

12

10

20

12 years

12 years

Explanation:

We are given;

Half life of hydrogen-3 is 12 years

Initial mass of Hydrogen-3 is 20 grams

Final mass will be 10 g because we are told half of the sample will decay.

To find the time taken for the decay we need to know what half life is;

Half life is the time taken for a radioactive isotope to decay to half its original amount. Using the formula;

Remaining mass = Original mass * 0.5^n

n = number of half lives

therefore;

10 g = 20 g * 0.5^n

0.5 = 0.5^n

n = log 0.5 : log 0.5

= 1

But, 1 half life is 12 years

Therefore, the time taken is 12 years