Question

Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.7 days. If you begin with a sample of 8.6 mg of the isotope, how much of this sample remains after 1.4 days?

Answer 1

Answer: 6.1 mg

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 = let initial amount of the reactant

a - x = amount left after decay process  

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.

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

$k=\frac{0.693}{2.7days}=0.26days^{-1}$

b) sample remains after 1.4 days

$1.4=\frac{2.303}{0.26}\log\frac{8.6}{a-x}$

$0.16=\log\frac{8.6}{a-x}$

$\frac{8.6}{a-x}=1.4$

$(a-x)=6.1mg$

The sample remains after 1.4 days is 6.1 mg