Question

Before the use of technetium-99m, patients with high risk coronary artery disease were evaluated using thallium-201 which has a half-life of 73.00 hours. If a person is exposed to 5.000 μg of thallium-201, how many hours would it take to reach 10.00 % of its original mass?

Answer 1

Answer: 243 hours

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

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

where,

k = rate constant

t = age of sample

a = initial amount of the reactant =
`5.000\mu g`

a - x = amount left after decay process =
`(10)/(100)* 5.000\mu g=0.5\mu g`

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

`t_{(1)/(2)}=(0.693)/(k)`

`k=(0.693)/(73.00hours)=9.49* 10^(-3)hours^(-1)`

b) for reducing the mass to 10.00 % of its original mass

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

`t=(2.303)/(9.49* 10^(-3))\log(5.000)/(0.5)`

`t=243hours`

The time taken to reach 10.00 % of its original mass is 243 hours