An experiment. is done to determine the half-life of a radioactive substance that emits one beta-particle for each decay process. Measurements show that an average of 8.4 beta-particles are emitted each second by 2.5 milligram of the substance. The atomic weight of the substance is 230. Find the half-life of the substance.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Find number of nuclei
Calculate the total number of nuclei ( 
) in the 2.5 mg sample using the atomic weight and Avogadro's number ( 
):
Determine decay constant
The decay rate (activity) is given as 8.4 beta-particles/s, which corresponds to 8.4 disintegrations/s since each decay emits one particle. Use the relationship 
to find the decay constant 
:
Calculate half-life
Use the half-life formula 
to find the time in seconds:
Convert to years
Convert the result from seconds to years:
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems