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Radioactive Decay


Hello Everyone!! I hope everyone is healthy and staying safe.  My mind is blown right now!!! I'm trying to figure out this decay problem that is in chapter 6 of the DOE Core Study Guide:
Can someone please tell me where I went wrong ?
A Phosphorous-32 source has a half-life of 14.28 days and had an activity of 75,000 dpm as of 12/2/92. What was the activity as of 12/28/92? The book answer is 21,230.9 dpm

So here is what I did:
Initial: 75,000 (7.5E4)
Elapsed: 26 days (28-2=26)
Half-life: 14.28 days
Final=7.5E4 x (.5)26/14.28
[/size](.5)^ 1.82=.2832 (or 2.832E-1)7.5E4 * 2.832E-1=2.124E4 (or 21,240)
My Answer is 21,240

It's a simple rounding issue. Without rounding any of the numbers, I got 21,230.85253174357 dpm which is in line with the book's answer.

Thanks RFaunt :)



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