Answer: The half life of the sample is 60.26 years.
Explanation:
All radioactive decay reactions follow first order reaction.
The formula used to calculate the rate constant for a first order reaction follows:
[tex]k=\frac{2.303}{t}\log \frac{a}{(a-x)}[/tex]
where,
k = rate constant = ?
t = time period = 25 years
a = initial concentration of the reactant = 500 g
a - x = concentration of reactant left after time 't' = (500 - 125) = 375 g
Putting values in above equation, we get:
[tex]k=\frac{2.303}{25yrs}\log \frac{500g}{375g}\\\\k=0.0115yr^{-1}[/tex]
Now, to calculate the half life period of the reaction, we use the equation:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
where,
[tex]t_{1/2}[/tex] = half life period of the reaction = ?
k = rate constant = [tex]0.0115yr^{-1}[/tex]
Putting values in above equation, we get:
[tex]t_{1/2}=\frac{0.693}{0.0115yr^{-1}}\\\\t_{1/2}=60.26yrs[/tex]
Hence, the half life of the sample is 60.26 years.
