Question

By mass spectral analysis, a sample of strontium is known to contain 2.64x10^10 atoms of Sr-90 as the only radioactive element. The absolute disintegration rate of this sample is measured as 1238 disintegrations per minute. The half-life (in years) of Sr-90 was found to be 28.49.

How long will it take (in years) for the disintegration rate of this sample to drop to 957 disintegrations per minute?

Answer 1

half life t1/2 = ln 2 / k      where k is decay constant

28.49 = ( 0.693 / k)

k = 0.02433 yr-

a= initial activity = 1238 dpm   ( disitintegration pe rminute)

a-x = 957 dpm = final activity

( we can use initial and final acvities or initial and final number of atoms in 1t order integration formula)

1st order kinectics is obeyed by decay constant

t = ( 1/k) ln ( a/a-x)

t = ( 1/0.02433 yr-1)   ln ( 1238 /957)

t= 10.58 years