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?
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%.
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