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

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

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

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

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

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) - Fe 55 line (5.89 keV) Linear Model: N = mE + b, N = bin # E = energy (keV)

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

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

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

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!

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

Experimental Design

E 1/2 = C (Z -  )

Comparison with Theoretical Model E 1/2 = C (Z -  ) K1K1 K2K2 K1K1 K2K2 C predicted C obtained0.11 § § 0.01 Bohr’s simple model of atomic energy levels is a sufficient approximation for the behavior of this system Why does the K  line split?

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 E 1/4 vs. Z fits a linear regression to a  2 of 3.5

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

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

Doublet Separation j = l + s -- vector sum: total angular momentum  E = R  2 (Z -  ) 4 / hn 3 l(l+1)

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

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.