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

For radioactive decay:

N = N(0) x exp(-λt), where λ is the decay constant equivalent to ln(2)/half life, N is the amount after a given amount of time, t is the time passed and N(0) is the initial amount.

1)
N = 24 x exp(-ln(2)/4.5 x 36)
N = 0.09375 mg

2)
1.2 = 9.6 x exp(-ln(2)/4.5 x t)
ln(1.2/9.6) = -t x ln(2)/4.5
t = 13.5 days