Question

The half-life of U-231 is 60 seconds. If one had 1000 g at the beginning, how many grams would be left after 4 minutes has elapsed?

Answer 1

Answer:

The half-life of U-231 is 60 seconds. If one had 1000 g at the beginning the amount left after 4 minutes is $60g$

Explanation:

• The half-life of a sample is the time required to react half of the sample, it is given by the formula

                   $T_{1/2}=\frac{0.693}{\lambda }$    λ-decay constant ( equation 1)

• Consider a sample with a half-life $T_{1/2}$ and  $N(0)$ be the beginning amount of sample at a later time $t$ the amount of sample would be

                 $N\left(t\right)=N\left(0\right)\ e^{-\lambda t}$

replace for the decay constant from equation 1

⇒

$N\left(t\right)=N\left(0\right)\ \frac{e^{-0.693t}}{T_{\frac{1}{2}}}$

From the question, we have

the initial amount of sample $N(0)=1000g=1kg$

the half-life of the sample $T_{1/2} =60s$

the at which the amount is to be calculated $t=4mnt=4*60s$

substitute these values, we get $N(t)=1*e^{-\frac{0.693*4*60}{60} } =\frac{1}{e^{2.76} }=0.06kg$