Question

Calcium-47, which decays by beta emission, has a half-life of 4.5days:How many milligrams of an initial 24mg of calcium-47 remain after 36days?

How many days are required for 9.60mg of calcium-47 to decay to 1.2mg?

Answer 1

\[N(t)=N_0*(0.5)^\frac{t}{t_{1/2}}\]\[N(36\ days)=(24mg)*(0.5)^\frac{36}{4.5}\]\[N(36\ Days)=0.094mg\]

Answer 2

\[N(t)=N_0*(0.5)^\frac{t}{t_{1/2}}\]\[1.2mg=9.60mg*(0.5)^\frac{t}{4.5day}\]\[0.125=0.5^\frac{t}{4.5day}\]\[\log_{0.5}0.125=\log_{0.5}0.5^\frac{t}{4.5day}\]\[\log_{0.5}0.125=\frac{t}{4.5day}\]\[3=\frac{t}{4.5day}\]\[t=13.5\ days\]