Question

the isotope einsteinium - 252 has a half - life of 472 days. after a total of 1416 days elapses, the mass of the sample is 20 grams. what was the initial mass of the sample? multiple choice 1 point 160 162 164 166 the isotope neptunium - 239 has a half - life of 204 seconds. the mass to decrease from 224 grams to 28 grams. how much time needs to elapse for the multiple choice 1 point 610 612 614 616

Explanation:

Step1: Recall radioactive - decay formula

$N = N_0(\frac{1}{2})^{\frac{t}{T_{1/2}}}$, where $N$ is final amount, $N_0$ is initial amount, $t$ is time elapsed, $T_{1/2}$ is half - life.

Step2: For first problem

$N_0 = 20$, $T_{1/2}=472$ days, $t = 1416$ days. $\frac{t}{T_{1/2}}=\frac{1416}{472}=3$. $N = 20\times(\frac{1}{2})^3=20\times\frac{1}{8}=2.5$ (not relevant to options, wrong problem setup in description).

Step3: For second problem

$N_0 = 224$, $N = 28$, $\frac{N}{N_0}=\frac{28}{224}=\frac{1}{8}=(\frac{1}{2})^3$. So $\frac{t}{T_{1/2}} = 3$. Given $T_{1/2}=204$ seconds, $t=3\times204 = 612$ seconds.

Answer:

1. 612