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 K1 and K2 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)

- Fe55 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

2E = .027 + 4*10-9(N -20.5)2

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

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/nf2 – 1/ni

2})

For K: ni=2 -> nf=1

E = 3/4Rhc(Z-)2

Experimental Design

E1/2 = C (Z - )

Comparison with Theoretical Model

E1/2 = C (Z - )

K1 K2 K1 K2

C predicted 0.101 0.101 0.110 0.113

C obtained 0.11 § 0.01 0.11 § 0.01 0.11 § 0.01 0.12 § 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

E1/4 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 = R2(Z - )4 / hn3l(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.