Measurements and Calculations (Introduction to Radiochemistry)

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Which detector did you use?

Background

Note down the values from the background counting you started the day before.
Counting number:
[math]N_{bck}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}[/math]
Counting time:
[math]t_{bck}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{sec}[/math]

Counting speed:
[math]\frac{N_{bck}}{t_{bck}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{cps}[/math]
Standard deviation:
[math]\frac{\sqrt{N_{bck}}}{t_{bck}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{cps}[/math]


Counting Efficiency

Do a one minute count on every shelf. Use these measurements to calculate the counting-efficiency of the GM-detector in %, for 234mPa. The activity of the sample can be calculated from the amount of UO3 used.


Counting number for each shelf (CPM) Counting Efficency
1

2

3

4


Twenty Measurements with Constant Distance from the Source

Do twenty measurements lasting for one minute with the source in the same position. Calculate the standard deviation and complete the table:

Nr [math]N_{P}\,[/math] [math]N_{P}-\overline{N}[/math] [math]\left(N_{P}-\overline{N}\right)^{2}[/math]
1


2


3


4


5


6


7


8


9


10


11


12


13


14


15


16


17


18


19


20


SUM:
SUM:



Mean value of the counting numbers
[math]\overline{N}=\frac{\sum N_{P}}{20}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}[/math]
The squere of the mean value [math]\sqrt{\overline{N}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}[/math]
Standard deviation [math]S_{N}=\sqrt{\frac{\sum\left(N_{P}-\overline{N}\right)^{2}}{19}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}[/math]
Discuss the results from [math]S_{N}\,[/math]and [math] \sqrt{\overline{N}}[/math]?

Assessment of the Results




Write down the given measurements and calculate how many % of the countings that are outside of the intervals <N-SN,N+SN&gt and <N-2SN,N+2SN>:

[math]\overline{N}[/math] [math]\sqrt{\overline{N}}[/math] [math]N\pm S_{N}[/math] [math]N\pm 2S_{N}[/math]









Is there, in your opinion, to many single measurements outside of the given areas? Give a answer based on statistical normal distribution.