If you had a 100-gram sample of plutonium, how much would still remain in 43 years?

Jun 7, 2016

${m}_{r} \cong 11.9 \setminus g r a m s$

Explanation:

What is missing from the question is the identity of the specific isotope present in the 100-gram sample - I would assume it is plutonium - 241 that has an average half-life of 14 years, the shortest among the plutonium isotopes family.

$n \text{ is the number of periods }$

$n = \frac{t i m e}{\text{half-life}}$

$n = \left(43 \setminus \text{years")/ (14 \ "years}\right) \cong 3.07$

${m}_{i} = {m}_{r} \times {2}^{n}$

${m}_{i} = \text{ is the initial mass}$

${m}_{r} = \text{ is the remaining mass after n periods}$

${m}_{r} = {m}_{i} / {2}^{n}$

${m}_{r} = \frac{100}{2} ^ \left(3.07\right)$

${m}_{r} \cong 11.9 \setminus g r a m s$