Respuesta :
Answer: 43.73 seconds
Explanation:
Half-life of indium = 14.10 sec
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{t_\frac{1}{2}}[/tex]
[tex]k=\frac{0.693}{14.10}=0.0491sec^{-1}[/tex]
Now we have to calculate the age of the sample:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = age of sample = ?
a = initial amount of the reactant = 7.70 mg= [tex]7700\mug[/tex]
[tex](1mg=1000\mug[/tex]
a - x = amount left after decay process = [tex]900\mug[/tex]
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{0.0491}\log\frac{7700}{900}[/tex]
[tex]t=43.73sec[/tex]
Thus it would take 43.73 seconds sample to decay from 7.70 mg to 900 µg.
