University:
Boston University
Course:
CAS CH 101 | General Chemistry 1
Academic year:

2023
Views:

91

Pages:

1
Author:

prodigalmehtusw

Half‐life calculations Fundamental relation (1/2)n N0 = N Half‐life example calculations 1. Half life is n for N/N0 = 1/2; independent of N0. 1 2. Given N/N0 after time t, calculate n, and then thalf = t/n 3. Given n, calculate N/N0, the fraction remaining after t = n thalf Half‐life calculations (1/2)n N0 = N Half‐life is 33 minutes. What fraction remains after 75 minutes? Strategy: Use n = 75/33 and then fraction remaining = N/N0 = (1/2)n Answer: n = 75/33 = 2.3, (1/2)n = 0.21 (21%) Half‐life calculations (1/2)n N0 = N A sample decays by 25% in 15 minutes. What Is its half‐life? Strategy: Use N/N0 = 0.75 and n = 15 min/thalf , solve N/N0 = (1/2)n for n = time/thalf , and so thalf = time/n Answer: n = − log(N/N0)/log(2) = − log(0.75)/log(2) = 0.415, hence thalf = 15/0.415 minutes = 36 minutes Half‐life calculations (1/2)n N0 = N Half‐life is 11 days. How long to decay by 10%? Strategy: Use N/N0 = 0.90, solve N/N0 = (1/2)n for n = time/thalf, and so time = n x thalf Answer: log[(1/2)n] = − n log(2) = log(N/N0) so n = − log(N/N0)/log(2) = − log(0.90)/log(2) = 0.152, hence, time = 0.152 x 11 days = 1.7 days Half‐life calculations Fundamental relation (1/2)n N0 = N CPS lesson: Half‐life examples