Please show all your work. If you upload an image please make sure it is clear a

Question

Please show all your work.

If you upload an image please make sure it is clear and your writing is legible.

Suppose you are trying to measure the rate of (total) decay events per second R from a certain radioactive source using a detector hooked up to a counter. You put the source in front of the detector and let it count for 70 seconds, and find that it has measured 537 events in that 70 s interval. Then you remove the source to measure the background decay rate (due to noise in the detector and natural radioactivity), and suppose you now count 211 events in a 90 s interval. Based on these measurements, what is your best estimate of (while thinking about Poisson Statistics and propagation of errors):

(a)  the decay rate R (of the source alone)

(b)  the uncertainty in R.

If you upload an image please make sure it is clear and your writing is legible. Suppose you are trying to measure the rate of (total) decay events per second R from a certain radioactive source using a detector hooked up to a counter. You put the source in front of the detector and let it count for 70 seconds, and find that it has measured 537 events in that 70 s interval. Then you remove the source to measure the background decay rate (due to noise in the detector and natural radioactivity), and suppose you now count 211 events in a 90 s interval. Based on these measurements, what is your best estimate of (while thinking about Poisson Statistics and propagation of errors): the decay rate R (of the source alone) the uncertainty in R.

Explanation / Answer

a)

537 in 70 sec

Rate = 537 / 70= 7.67 which is 8 counts /sec

background = 211/90= 2.344 = 2 counts /sec

effective decay rate = 8-2= 6 counts /sec

b) uncertainity in R = sqrt (R)= sqrt(6) = 2.44

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