Respuesta :
The question is incomplete, here is the complete question:
The half-life of a certain radioactive substance is 46 days. There are 12.6 g present initially.
When will there be less than 1 g remaining?
Answer: The time required for a radioactive substance to remain less than 1 gram is 168.27 days.
Step-by-step explanation:
All radioactive decay processes follow first order reaction.
To calculate the rate constant by given half life of the reaction, we use the equation:
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
where,
[tex]t_{1/2}[/tex] = half life period of the reaction = 46 days
k = rate constant = ?
Putting values in above equation, we get:
[tex]k=\frac{0.693}{46days}\\\\k=0.01506days^{-1}[/tex]
The formula used to calculate the time period for a first order reaction follows:
[tex]t=\frac{2.303}{k}\log \frac{a}{(a-x)}[/tex]
where,
k = rate constant = [tex]0.01506days^{-1}[/tex]
t = time period = ? days
a = initial concentration of the reactant = 12.6 g
a - x = concentration of reactant left after time 't' = 1 g
Putting values in above equation, we get:
[tex]t=\frac{2.303}{0.01506days^{-1}}\log \frac{12.6g}{1g}\\\\t=168.27days[/tex]
Hence, the time required for a radioactive substance to remain less than 1 gram is 168.27 days.
