Question

The isotope 208^Tl undergoes β decay with a half-life of 3.1 min.
(a) What isotope is produced by the decay?
(b) How long will it take for 99.0% of a sample of pure 208Tl to decay?
(c) What percentage of a sample of pure 208Tl remains un-decayed after 1.0 h?

Answer 1

half life = 3.2 min

a) when β decay is possible, atomic number decreases by one unit and no change in mass number.

atomic number of Tl = 81

₈₁Tl ²⁰⁸ ------------------- ₈₀ Hg ²⁰⁸ + β decay               β particle is _-1 e ⁰

₈₁Tl ²⁰⁸ ------------------- ₈₀ Hg ²⁰⁸ + _-1 e ⁰

Mercury Isotope is formed after β decay .

b)

a= 100%

a-x = 100 - 99= 1.0%

half life = 0.693 / k

k = 0.693 / t1/2

k = 0.693 / 3.1 = 0.223 min-1

k = 2.303/t log( a/a-x)

t= 2.303/k log(a/a-x)

t= 2.303 / 0.223 log( 100/1.0)

t= 20.65 min

c)

t= 1.0 h = 60 min

k = 2.303/t log( a/a-x)

0.223 = 2.303/ 60 log( 100/100-x)

log( 100/100-x) = 5.81

100/100-x = 645654.23

100 = 64565423 - 645654.23 x

x= 99.99

remaining percentage = 0.01%.