Answer: 75.8 %
Explanation:
Half-life of tritium= 12.33 years
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{12.33\text{years}}[/tex]
[tex]k=0.056\text{years}^{-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 = [tex]0.056\text{years}^{-1}[/tex]
t = age of sample = 5 years
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = a g
Now put all the given values in above equation, we get
[tex]5=\frac{2.303}{0.056}\log\frac{100}{a}[/tex]
[tex]a=75.8[/tex]
[tex]a=\frac{75.8}{100}\times 100=75.8\ %[/tex]
Thus 75.8 percentage of a sample will remain after 5 years have passed.
