The "third-life," the time it takes nuclei to decay until one-third of the original amount remains,expressed in terms of the decay constant $\beta$,is
A)(ln 2)/3$\lambda$
B)(ln 3)/$\lambda$
C)(ln 0.333)/$\lambda$
D)3(ln 2)/$\lambda$
E)$\lambda$/3

Question

Quizplus · Accepted Answer

The formula for the time it takes for a certain fraction of a radioactive sample to decay is given by $ t = \frac{\ln(\frac{1}{fraction\ remaining})}{\lambda} $, where $ \lambda $ is the decay constant. For the third-life, where one-third of the original amount remains, the fraction remaining is $ \frac{1}{3} $. Thus, the time is $ t = \frac{\ln(3)}{\lambda} $, making option B correct.

The "Third-Life," the Time It Takes Nuclei to Decay Until β\betaβ

The "Third-Life," the Time It Takes Nuclei to Decay Until $\beta$