Nuclear Chemistry

Step 1: Understanding the Problem
A first
order reaction is half completed in 45 minutes. We need to find the time required for 99.9\% of the reaction to be completed.
Step 2: Using the Half
Life Formula for First
Order Reactions
The half
life ( ) of a first
order reaction is given by: where is the rate constant.
Step 3: Calculating the Rate Constant
Given minutes:
Step 4: Using the First
Order Reaction Formula
The first
order reaction formula is: where:
is the initial concentration,
is the concentration at time ,
is the rate constant,
is the time.
Step 5: Calculating the Time for 99.9\% Completion
For 99.9% completion, .
Substituting into the first
order reaction formula:
Substituting :
Converting minutes to hours:
Step 6: Matching with the Options
The calculated time is 7.5 hours, which corresponds to option (B). Final Answer: The time required for 99.9\% of the reaction to be completed is (B) 7.5 hours.