Physics 145
Introduction to Experimental Physics I
Instructor: Karine Chesnel
Office: N319 ESC
Tel: 801- 422-5687
kchesnel@byu.edu
Office hours: on appointment
Class website:
http://www.physics.byu.edu/faculty/chesnel/physics145.aspx
Your lab assignments
1. Prepare by reading the introduction material
2. Answer quiz questions (within the first half hour) and
submit the sheet to your TA
3. Proceed to the experiments: L2.1, L2.2, etc…
4. Write a report of your findings for each experiment,
in your lab notebook (individual reports)
Lab 4/ Lab 5
Radioactivity
Curve fitting
Error propagation
Curve fitting
Experimental data
Linear fit
Attempts for fitting
the experimental curve
Curve fitting:
Examples in crystallography
Identify different peaks in a spectrum
28.5
29.0
29.5
2q(deg.)
CexZr1-xO2
0<x<1
45
30.0
ZrO2
46nm
CeO2
19 nm
Intensity (a.u.)
Intensity (a.u.)
Fit a diffraction peak:
46
47
48
49
2q(deg.)
Intensity (a.u.)
00-043-1002> Cerianite- - CeO 2
Being able to separate
peaks in a spectrum
23
24
25
26
27
28
29
30
31
32
33
2q (deg.)
34
35
36
37
38
39
40
41
50
51
52
Lab experiment:
Radioactivity
a - rays
(4He nuclei)
b - rays
(electrons)
- rays
(photons)
Lab experiment:
Radioactivity
Aluminum shield
or
Lead shield
- rays
(photons)
Lab experiment:
Radioactivity
- rays
N
Radioactive decay:
N
  N
t
R
R0 /2
N (t )  N 0 e  t
Decay rate:
R(t )  R0e  t
t
T1/2
Half-life:
T1/ 2 
ln 2

Lab experiment:
Radioactivity
x1
x2
Counts: N1
N
Counts: N2
X
Radiation absorption
Number of
particles absorbed:
Decay rate:
N
 N
x
R ( x)  R0 e   x
R
R0 /2
x
x1/2
Half-length:
x1/2 
ln 2

Lab 4: Radioactivity- curve fitting
A. Experiment
• L4.1: get familiar with the equipment:
137Cs
source, counting chamber,
and Geiger counter
• L4.2: Background radiation counts RB
• L4.3: Qualitative measure of absorption decay
using aluminum sheets
Lab 4: Radioactivity- curve fitting
B. Quantitative measure of hal-length in lead
• L4.4: Measure counts for varying thicknesses (get ~20 points)
Make sure to measure the thicknesses and count for at least 60 sec
• L4.5: Plot your results in Excel spreadsheet:
Thickness (x), time (T), counts (N), rate (R=N/T) , ln (R-RB)
• L4.6: plot R as function of x
• L4.7: plot ln (R-RB) as function of x
• L4.8: fit with linear regressionuse the parameters of fit to estimate:
- absorption coefficient 
- half length in lead
Lab 4: Radioactivity- curve fitting
B. Perform non –linear least square fit
• L4.9: Copy your data in Logger Pro:
Plot Rate as function of thickness
• L4.10: use logger Pro to do an exponential fit
use the parameters of fit to estimate:
- absorption coefficient 
- half length in lead
- the background radiation RB
Compare results from linear fit and exponential fit
Experimental uncertainties
Uncertainty =
Accuracy
+
Difference between
Measured/
Expected value
- Histogram
- Gaussian distribution
- Poisson distribution
- mean value
- standard deviation / variance
Precision
Instrument Resolution
Statistical Error
Uncertainty propagation
Gaussian error propagation
 f 
If
2
2
 f 
 f 
    a      b   ...
 a 
 b 
2
2
f  a  b  ...
2
then
 f    a    b   ...
2
2
If
f  a j bk ...
then
2
2
 f 
2  a 
2  b 

j

k





  ...
 a 
 b 
 f 
2
2
Lab 5: Radioactivity- experimental uncertainty
• L5.1: Reapeat counts measurements 100 times (10 sec each)
• L5.2: Make an histogram
• L5.3- 5: analyze distribution
• L5. 6- 8 : propagation of error, N , T and rate R
• L5.8: perform an non-linear least square fit with error included
use the parameters of fit to estimate:
- absorption coefficient 
- half length in lead
- Background counts