Physics 145 Introduction to Experimental Physics I Instructor: Karine Chesnel Office: N319 ESC Tel: Office hours: on appointment Class website:

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  (deg.) Intensity (a.u.) > Cerianite- - CeO 2 CeO 2 19 nm  (deg.) Intensity (a.u.) ZrO 2 46nm Ce x Zr 1-x O 2 0<x<1 Fit a diffraction peak: Identify different peaks in a spectrum Being able to separate peaks in a spectrum

Lab experiment: Radioactivity  - rays ( 4 He nuclei)  - rays (electrons)  - rays (photons)

Lab experiment: Radioactivity Aluminum shield or Lead shield  - rays (photons)

Lab experiment: Radioactivity Radioactive decay: N Decay rate:  - rays R t Half-life: R 0 /2 T 1/2

Lab experiment: Radioactivity Radiation absorption N Decay rate: Counts: N 1 R x Half-length: R 0 /2 x 1/2 X Number of particles absorbed: Counts: N 2 x1x1 x2x2

Lab 4: Radioactivity- curve fitting A. Experiment L4.1: get familiar with the equipment: 137 Cs source, counting chamber, and Geiger counter L4.2: Background radiation counts R B L4.3: Qualitative measure of absorption decay using aluminum sheets

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-R B ) L4.6: plot R as function of x L4.7: plot ln (R-RB) as function of x L4.8: fit with linear regression- use 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 R B Compare results from linear fit and exponential fit

Uncertainty = Accuracy + Precision Difference between Measured/ Expected value Instrument Resolution Statistical Error Experimental uncertainties - Histogram - Gaussian distribution - Poisson distribution - mean value - standard deviation / variance

Uncertainty propagation Gaussian error propagation Ifthen Ifthen

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 L : 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