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

Explanation:

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

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

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 =  $\frac{10}{100}\times 5.000\mu g=0.5\mu g$

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.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{73.00hours}=9.49\times 10^{-3}hours^{-1}$

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

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

$t=\frac{2.303}{9.49\times 10^{-3}}\log\frac{5.000}{0.5}$

$t=243hours$

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