The heaviest known isotope of hydrogen is called tritium, . It decays by beta emission, and has a half-life of 12.3 years. What fraction of a tritium sample will remain after 5.20 years ?

Question

The heaviest known isotope of hydrogen is called tritium,  . It decays by beta emission, and has a half-life of 12.3 years. What fraction of a tritium sample will remain after 5.20 years ?

Quizplus · Accepted Answer

We can use the radioactive decay formula to solve this problem:

N(t) = N0 e^(-λt)

where N(t) is the amount of tritium remaining after time t, N0 is the initial amount of tritium, λ is the decay constant (which we can find from the half-life), and e is the mathematical constant approximately equal to 2.71828.

First, we need to find the decay constant:

t1/2 = ln(2)/λ

12.3 years = ln(2)/λ

λ = ln(2)/12.3 years ≈ 0.0565 years^-1

Now we can use the formula to find the amount of tritium remaining after 5.20 years:

N(5.20) = N0 e^(-0.0565*5.20)

N(5.20)/N0 = e^(-0.2942)

N(5.20)/N0 ≈ 0.746

So about 74.6% of the original tritium sample will remain after 5.20 years.

Therefore, the best choice is B) 0.746.

The Heaviest Known Isotope of Hydrogen Is Called Tritium