Question

Question 9 (8 points) A sample of a radioactive compound initially emits 35.8 Bq. After 25.7 days, the level has fallen to 13.8 Bq. What is the half life of the compound?

Answer 1

we have:

[A]o = 35.8 Bq

[A] = 13.8 Bq

t = 25.7 days

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k*t

ln(13.8) = ln(35.8) - k*25.7

2.625 = 3.578 - k*25.7

k*25.7 = 0.9533

k = 3.709*10^-2 days-1

Given:

k = 3.709*10^-2 days-1

use relation between rate constant and half life of 1st order reaction

t1/2 = (ln 2) / k

= 0.693/(k)

= 0.693/(3.709*10^-2)

= 18.68 days

Answer: 18.7 days