Question

188Re has a half-life of 17.0 hr. How long will it take for 5 mg of the isotope to decay to 0.5 mg?

a. 56 hr

b. 27 hr

c. 9.4 hr

d. 0.094 hr

e. 5.6 hr

Answer 1

we have:

Half life = 17 hr

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

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(17)

= 4.076*10^-2 hr-1

we have:

[Re]o = 5.0 mg

[Re] = 0.5 mg

k = 4.076*10^-2 hr-1

use integrated rate law for 1st order reaction

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

ln(0.5) = ln(5) - 4.076*10^-2*t

-0.6931 = 1.6094 - 4.076*10^-2*t

4.076*10^-2*t = 2.3026

t = 56 hr

Answer: a