- #1
Albo1125
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Hi all,
I have a question concerning the derivative of the formula of the number of nuclei. I hope I've posted this in the right section, I'm new here :P. Anyway, in the question, the given values are:
At a certain time t, there is an amount of radioactive Br-82. The activity A is 7.4*1014 Bq, the number of nuclei N is 9.6*1018.
I'm meant to calculate t1/2, the time it takes before the number of nuclei has halved.
N = N0 * (½)t/t1/2
The derivative of the formula above (given by the coursebook, so it's correct): A = ( ln(2) * N) / t1/2.
What seemed like a plausible solution to me was to use the derivative to calculate t1/2.
So: t1/2 = ( ln(2) * N) / A.
That gave me: t1/2 = ( ln(2) * 9.6*1018 ) / ( 7.4*1014) = 8992 seconds. This derivative always uses t1/2 in seconds.
This is equivalent to 8992/3600 = 2.50 hours. So t1/2 = 2.50 hours.
The correct answer, however, is 35.3 hours.
Can anybody explain what mistake I have made, or why I can't use the derivative in this situation?
Thank you very much in advance :)
I have a question concerning the derivative of the formula of the number of nuclei. I hope I've posted this in the right section, I'm new here :P. Anyway, in the question, the given values are:
At a certain time t, there is an amount of radioactive Br-82. The activity A is 7.4*1014 Bq, the number of nuclei N is 9.6*1018.
I'm meant to calculate t1/2, the time it takes before the number of nuclei has halved.
Homework Equations
N = N0 * (½)t/t1/2
The derivative of the formula above (given by the coursebook, so it's correct): A = ( ln(2) * N) / t1/2.
The Attempt at a Solution
What seemed like a plausible solution to me was to use the derivative to calculate t1/2.
So: t1/2 = ( ln(2) * N) / A.
That gave me: t1/2 = ( ln(2) * 9.6*1018 ) / ( 7.4*1014) = 8992 seconds. This derivative always uses t1/2 in seconds.
This is equivalent to 8992/3600 = 2.50 hours. So t1/2 = 2.50 hours.
The correct answer, however, is 35.3 hours.
Can anybody explain what mistake I have made, or why I can't use the derivative in this situation?
Thank you very much in advance :)