1. Experiments in X-Ray Physics Lulu Liu Partner: Pablo Solis Junior Lab 8.13 Lab 1 October 22nd, 2007

2. Discovery of X-Rays • Wilhelm Roentgen (1895) image from Cathode Ray Tube Site image from Wolfram Research • Penetrating High Energy Photons • Bremsstrahlung Radiation

3. High Energy Photons and Matter • Production • Bremsstrahlung Radiation (Continuum) • Atomic and Nuclear Processes (Radioactive Decay) • Fluorescence • Characteristic Lines (Inner Shell) • Scatter • Photoelectric Effect (<50 keV) • Compton Scattering (50 keV to 1 MeV) • Pair Production (> 5 MeV) pair production from the wikipedia commons

4. Why X-Ray Physics? • Characteristic energy range of many atomic processes and transitions - regularity • Interacts with matter in many ways • easy to produce and characterize • scattered and absorbed by all substances • Medium penetration power • region of interest is normal matter, can be tuned, medicine

5. Presentation Outline • Calibration of Equipment and Error Determination • Production of X-Rays: • Bremsstrahlung and e- e+ Annihilation • X-Ray Fluorescence • Motivation and Experimental Set-up • Energy of Characteristic Lines vs. Atomic Number (Z) • Doublet Separation between K1 and K2 lines • Error and Applications

6. Equipment and Calibration • Germanium Solid-State Detector and MCA • Energy Calibration (optimally three points) • For characteristic lines: - Tb K line (44.5 keV) - Mo K line (17.5 keV) - Fe55 line (5.89 keV) • Linear Model: N = mE + b, N = bin # E = energy (keV)

7. Calibration Fit 2 of 2.6 Linear fit to determine energy and error on energy 2E = .027 + 4*10-9(N -20.5)2 Different calibration for each range

8. Bremsstrahlung Production • E(b) (impact parameter) • Continuous Spectrum • E max = Ke- max Strontium-90 Source/Lead Target n -> p+ + e- + e’ Sr90 -> Y90 -> Zr90 max 2.25 MeV plot from lab guide

9. Bremsstrahlung Spectrum and Results Theoretical Value: 2.25 MeV - energy loss in trajectory - detector efficiency

10. Characteristic Lines - Motivation • X-Ray fluorescence of elements • sharp peaks, independent of incident energy • uniquely characterizes an element • low variability of spectrum – shift • How are they produced? • What is the relation? ATOMIC STRUCTURE!

11. Characteristic Lines Hypothesis • Innermost-shell electron transitions • Ionization • Bohr Model Energy Level Approximation: E = Rhc(Z-)2 (1/nf2 – 1/ni2}) For K: ni=2 -> nf=1 E = 3/4Rhc(Z-)2 Image courtesy of Nuclear Society of Thailand

12. Experimental Design

14. E1/2 = C (Z - )

15. Comparison with Theoretical Model E1/2 = C (Z - ) Bohr’s simple model of atomic energy levels is a sufficient approximation for the behavior of this system Why does the K line split?

16. Doublet Separation • Briefly: spin-up and spin-down electrons in same n and l state have slightly different energies! E = C’(Z - ’)4 from Compton and Allison E1/4 vs. Z fits a linear regression to a 2 of 3.5

17. Statement on Error • Dominated by calibration error - a systematic that includes random error • Too few calibration points (Pb) – large error

18. Conclusions and Applications • K-line emission a result of inner shell electron transitions (to n=1) • Strong quadratic relationship (E vs. Z) • Each element – unique K line energies • compositional analysis technique • Determine atomic numbers of elements • predict the existence of elements

21. Doublet Separation • j = l + s -- vector sum: total angular momentum E = R2(Z - )4 / hn3l(l+1)

22. Relative Intensities Statistical weight: 2j + 1 for n = 1 state transitions: Relative intensity = ratio of statistical weights K-alpha: 4/2 = 2

23. Germanium Solid State Detector • p-type doping: impurities that only makes 3 bonds w/ Ge, leaving a charge carrying hole • n-type doping: impurities that want to make 5 bonds, unsaturated, charge carrier – adds electron close to conduction band • p-n junction, p-part neg wrt n – no current flow – reverse bias.