Question

after 30 hours a sample of Plutonium-243, has decayed to (1/64) of its original mass. find its half life.

Answer 1

960 hr?

Answer 2

since it;s decay, we use
\[\ln (\frac{x_0}{x}) = kt\]
after 30 hours x = 1/64 x_0

\[\ln (\frac{x_0}{\frac{1}{64}x_0}) = 30k\]
\[\ln (\frac{1}{\frac{1}{64}}) = 30k\]
\[\ln (64) = 30k\]
\[k = \frac{\ln (64)}{30}\]
now to find half-life use \[t_{1/2} = \frac{\ln 2}{k}\]
\[t_{1/2} = \frac{\ln 2}{\frac{\ln(64)}{30}}\]
\[t_{1/2} = \frac{30\ln 2}{\ln (64)}\]

use a calculator to solve this

Answer 3

thanks