Question

A radioactive isotope (239)Pu has a half life of 24,360 years. What is the initial amount of the isotope if there is only 4.2 grams left after 1,000 years?

please show all work\

Answer 1

Y(t)= = Y(0) e^kt
Y(0) = ?

Answer 2

sub the values for the time vs the size

Answer 3

so Y(t)=4.2 when t =1000

Answer 4

substitute the value of the half life at t=24360

Answer 5

\[4.2=Q_0\times (\frac{1}{2})^{\frac{1000}{24360}}\]
\[Q_0=4.2\div(\frac{1}{2})^{\frac{1000}{24360}}\]