Question

The first-order decay of radon has a half-life of 3.823 days. How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

Answer 1

substitute: \(\large t_{1/2}=\dfrac{ln(2)}{k}\rightarrow k=\dfrac{ln(2)}{t_{1/2}}\)

Into the appropriate equation: \(\large [A]_t=[A]_0*e^{-kt}\)


\(\Large [A]_t=[A]_0*e^{-\frac{ln(2)}{t_{1/2}}t}\)

\(\Large [A]_t=(250.0 ~g)*e^{-\frac{ln(2)}{3.823~ days}(7.22~ days)}=67.52~g\)