Compton Scattering Aim The aim of this experiment is to look at how scattering angle is related to photon energy in Compton Scattering. We will then use these results to deduce the mass of an electron. Skills checklist At the end of this experiment you should: Understand how scattering angle and photon energy are related Have a basic understanding of CASSY LAB Be able to use a MathCad program for analysing data Introduction A phenomenon called Compton Scattrering, first explained in 1923 by the American physicist A.H Compton, provides additional direct confirmation of the quantum nature of X-rays. When the X-rays strike matter, some of the radiation is scattered, just as visible light falling on a rough surface undergoes diffuse reflection. Compton and others discovered that some of the scattered radiation has smaller frequency (longer wavelength) than the incident radiation and that the change in wavelength depends on the angle through which the radiation is scattered. Specifically, if the radiation emerges at an angle θ with respect to the incident direction and if λ/e and λ` /E` are the wavelengths/energies of the incident and scattered radiation, respectively, we find that Or Where m is the electron rest mass, and h is Planck s constant. The quantity h/mc that appears in the equation has units of length. Its numerical value is
This is known as the Compton Wavelength. Experimental Set-up Ensure that the experiment is set up as follows: The voltage source must be set to provide 0.7 Kvolts. Why are the lead blocks used? Equipment list 1x sensor CASSY 1x CASSY LAB 1x MCA 1x equipment set Compton 1x CS-137 preparation 1x scintillation counter Safety note You ll be using a hot gamma source (Caesium-137) and this must be handled safely. Return the source to technicians whenever the experiment is left unattended Do not try and remove the aluminium shielding protecting the source
The Experiment Calibration: - you will notice that the horizontal axis on the CASSY has not been calibrated for the energy of the source. To do so, take a reading for 300s with only the source (no target). You will get a distribution as follows like that to the left. Using the right hand button on the mouse select energy calibration. A line will appear on the screen, place this at peak 1. Set the energy to 662.66KeV. Repeat this for peak at 2 and set energy at 32.19KeV. The experiment: - Place the gamma source at equal intervals along the centre. At each position; Record the count for a period of time with the aluminium target in place Repeat this without the aluminium target Go to the overview tab Right click and create a new spectrum which shows us only the radiation refracted from the target. Given time constraints, how many positions do you think are suitable? What about the period of time for each recording? Whilst CASSY is recording, you may like to investigate Compton Scattering further. Below is a list of useful resources. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html#c1 http://www.ndted.org/educationresources/communitycollege/radiography/physics/compto nscattering.htm For a more general introduction to radioactivity: http://physics.isu.edu/radinf/gamma.htm
http://www.ndted.org/educationresources/communitycollege/radiography/physics/gamma. htm Analysing the data Go to Start My Network places PhyLabs Y1 Data analysis ISQ3_3. This is the MathCad programme you can use to analyse the data collected We know that angle and energy are related as follows Where: E is energy of incident photons (constant) E` is energy of refracted photons (at peak of spectrum) θ is the angle the photons are scattered through m is mass of the electron Ton analyse the data, we want to manipulate the formula so that θ and E` are related linearly, ie, by a straight line of the form y = mx + c Where m is gradient, c is intercept, y = f(e`) and x = f(θ) Think of how the formula can be adjusted to give the above format. Input suitable values for x and y into the table. You should have two readings for the same angle (30 and -30 for example) ; take their mean. Should you use your results for an angle of 0 degrees. Why / why not? The errors can be calculated by taking the differance of your two results for each angle (mean of 30 and -30 for example) multiplying by 0.7 Why do we not just look at the spread of just one of the energy distributions.when calculating error? Why would we choose to multiply by 0.7? This is not the error on y. Knowing that Where does this come from?
And differentiating your formula for y = f(e ) you can calculate σy for each position. Should we put an error on the angle of refraction measured also? Input this into the error column. Click on area outside of the table and scroll down to see the two plots generated. Is the fit to data good? Did you under- or over-estimate errors? Are there enough data points? Which other areas have we not considered? Use the value of the gradient to help calculate your value for the mass of the electron. Remember that you have been working in KeV!! Use the intercept as a check; does it give the same value for E as you specified when calibrating the experiment?