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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 Cathode Ray Tube Site. image from Wolfram Research. Penetrating High Energy Photons. Bremsstrahlung Radiation.

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experiments in x ray physics

Experiments in X-Ray Physics

Lulu Liu

Partner: Pablo Solis

Junior Lab 8.13 Lab 1

October 22nd, 2007

discovery of x rays
Discovery of X-Rays
  • Wilhelm Roentgen (1895)

image from Cathode Ray Tube Site

image from Wolfram Research

  • Penetrating High Energy Photons
  • Bremsstrahlung Radiation
high energy photons and matter
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
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
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
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)

calibration fit
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

bremsstrahlung production
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

bremsstrahlung spectrum and results
Bremsstrahlung Spectrum and Results

Theoretical Value: 2.25 MeV

- energy loss in trajectory

- detector efficiency

characteristic lines motivation
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
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

comparison with theoretical model
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?

doublet separation
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

statement on error
Statement on Error
  • Dominated by calibration error - a systematic that includes random error
  • Too few calibration points (Pb) – large error
conclusions and applications
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 separation21
Doublet Separation
  • j = l + s -- vector sum: total angular momentum

E = R2(Z - )4 / hn3l(l+1)

relative intensities
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
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.