Question

The radioactive isotope 210 Bi 83 decays by alpha emission.

If the mass of a sample of bismuth-210 decays from 99.1 micrograms to 12.4 micrograms in 15.0 days, what is the half-life of bismuth-210?

Half-life = days

Answer 1

we have:

[Bi-210]o = 99.1 M

[Bi-210] = 12.4 M

t = 15.0 days

use integrated rate law for 1st order reaction

ln[Bi-210] = ln[Bi-210]o - k*t

ln(12.4) = ln(99.1) - k*15

2.5177 = 4.5961 - k*15

k*15 = 2.0784

k = 0.1386 days-1

we have:

k = 0.1386 days-1

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

t1/2 = (ln 2) / k

= 0.693/(k)

= 0.693/(0.1386)

= 5.00 days

Answer: 5.00 days