The heaviest known isotope of hydrogen is called tritium, H. 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,  H. 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 formula for exponential decay: N(t) = N0*exp(-λ*t), where λ is the decay constant and t is time. The half-life formula is: T1/2 = ln(2)/λ, which we can rearrange to find λ = ln(2)/T1/2.

For tritium, T1/2 = 12.3 years and λ = ln(2)/T1/2 = 0.0564 per year.
Let's say we start with N0 particles of tritium. After 5.20 years, we will have: 
N(5.20) = N0*exp(-λ*5.20) particles remaining. 
Plugging in the numbers: N(5.20) = N0*exp(-0.0564*5.20) = 0.746*N0.

Therefore, the fraction of the tritium sample that remains after 5.20 years is 0.746, which is choice B.

The Heaviest Known Isotope of Hydrogen Is Called Tritium