Transcript Final presentation - high school teachers at CERN

Workgroup Practical Activities:
Cosmic Rays
Ela, Helena, Jef, Leo, Carlos
Thanks to Jack, Stacy and Tom
Content
1/ PowerPoint presentation for Teachers and
Students
2/ Determination of the speed of muons
3/ Correlation between flux and distance
1/ PowerPoint presentation for
Teachers and Students
See: PowerPoint presentation for Teachers and Students.ppt
2/ Determination of the speed of
muons
Setup
We looked for coincidences
 hit?
 time-window of 192 ns
 2nd hit?
 coincidence!
BUT ...
This can also happen:
plate 1
plate 2
Probability???
 1st part of the experiment: determination of probability
 (2st part of the experiment: determination of speed)
1st part of the experiment:
We determined:
(average) number of hits on CH1 (per minute)
(average) number of hits on CH2 (per minute)
(average) number of coincidences (per minute)
Results:
CH1: 1150 hits / min
CH2: 4074 hits / min
Number of coincidences: 90 / min
Statistical analysis
CH1: 1150 hits / min
Poissondistribution:
P (k, λ) =
Prob of at least 1 hit on CH1 in 192 ns = 3,68 x10-6
Prob of at least 1 hit on CH2 in 192 ns = 1,30 x10-5
Prob of at least1 hit on CH1 AND on CH2 in 192 ns:
3,68 x10-6 x 1,30 x 10-5 = 4,78 x 10-11
1 coinc in 0,67 s
90 coinc per minut
1 coinc in 1 h 07 min
‘ALL’ coincidences are
caused by particles going
through both plates
2nd part of the experiment:
When there was a coincidence, we determined:
– the channel number
– the time of the rising edge (t1 and t2)
We calculated t2 - t1.
Results:
number of time differences = 1428
MIN = 0.491 ns
MAX = 11.748 ns
AVERAGE = 3.422 ns
STDEV = 2.187 ns
v = (1,88 ± 1,20) x 108 m/s
Analysis
Expected distribution:
Distribution we got:
Possible explanations:
1: not all the muons travel with the ‘same’ speed
2: the error on the time-differences
Time-diff ≈ ** ns ± 2 ns
Average = 3.422 ns ± 2.187 ns
How to improve the experiment?
If we could measure the time-differences as accurate
as the distance, we should have an error
on the speed as low as
0,020 x 108 m/s!
Useful and practicable?
+
Opportunity of
- use of statistics
- experiment from mod.phys.
- deep analysis of setup,
method, results
- start of CR-project
- work with high-tech equipment
- equipment
- curriculum
3/ Correlation: number of coincidences
and distance between two detectors
Table and graph of results
Distance
(m)
0.25
0.4
0.6
0.9
1.2
1.8
2.4
3
3.6
4.2
4.8
5.4
Number of
coincidences
(per 6 min)
333
150
67
40
26
20
10
8
12
7
4
6
Analyzing data
Number of coincidences versus distance
NOC
600
500
y = 40.993 x-1.3118
R2 = 0.9673
400
300
200
100
distance (m)
0
0
1
2
3
4
5
6
The exponent is rather strange:
- 1.3118
Possible explanations:
- during time of measurement, there is not only
one shower, but also others, so that there is no
fixed relationship (e.g. NOC ~ x-2 )
To investigate this, we have to repeat the
experiment and check whether the exponent
remains the same, and if not, to see if these
numbers are distributed at random.
- background
After subtracting background from the results
Now we got for the exponent -1.9417
-1.94 ≈ - 2
NOC ~ 1 / x² ???
It was only one experiment with 7 measurement
points, that is not enough to find the ‘real’
correlation.
More measurements in different conditions are
advised.