Question

After 300 years of decay, only 22 grams of an isotope remain from an original sample of 100 grams. How long is the half life?

Answer 1

The half life formula:

A = A' * (0.5)^(t/r)

Where A' is the initial value and r is half life

So,

given:

After 300 years of decay, only 22 grams of an isotope remain from an original sample of 100 grams

So, A' = 100 gram, A = 22 gram and t = 300 years

so,

22 = 100 * (0.5)^(300/r)

(0.5)^(300/r) = 22/100 = 0.22

take ln for both sides

300/r = (ln 0.22)/(ln 0.5) = 2.184

so,

r = 300/2.184 = 137.34 years