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

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

`k=(0.693)/(2.7days)=0.26days^(-1)`

b) sample remains after 1.4 days

`1.4=(2.303)/(0.26)\log(8.6)/(a-x)`

`0.16=\log(8.6)/(a-x)`

`(8.6)/(a-x)=1.4`

`(a-x)=6.1mg`

The sample remains after 1.4 days is 6.1 mg