Part A You are using a Geiger counter to measure the activity of a radioactive s
ID: 552558 • Letter: P
Question
Part A You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400 counts has diminished to 100. counts after 83.4 minutes , what is the half-life of this substance? Express your answer with the appropriate units Hints t1/2= 1 Value Units Submit My Answers Give Up Part B An unknown radioactive substance has a half-life of 3.20 hours. If 43.8 g of the substance is currently present, what mass Ao was present 8.00 hours ago? Express your answer with the appropriate units Hints |Ag= Value Units Submit My Answers Give UpExplanation / Answer
A)
we have:
[A]o = 400
[A] = 100
t = 83.4 min
use integrated rate law for 1st order reaction
ln[A] = ln[A]o - k*t
ln(100) = ln(400) - k*83.4
4.6052 = 5.9915 - k*83.4
k*83.4 = 1.3863
k = 1.662*10^-2 min-1
we have:
k = 0.0166 min-1
use relation between rate constant and half life of 1st order reaction
t1/2 = (ln 2) / k
= 0.693/(k)
= 0.693/(1.662*10^-2)
= 41.7 min
Answer: 41.7 minutes
B)
we have:
Half life = 3.2 hours
use relation between rate constant and half life of 1st order reaction
k = (ln 2) / k
= 0.693/(half life)
= 0.693/(3.2)
= 0.2166 hours-1
we have:
[A] = 43.8 g
t = 8.0 hours
k = 0.2166 hours-1
use integrated rate law for 1st order reaction
ln[A] = ln[A]o - k*t
ln(43.8) = ln[A]o - 0.2166*8
ln[A]o = 3.7796 + 0.2166*8
ln[A]o = 5.5121
[A]o = 248 g
Answer: 248 g
Feel free to comment below if you have any doubts or if this answer do not work