How Does Compton Scattering Affect X-ray and Gamma-ray Wavelengths?

[jennyhelp]

Homework Statement

X-ray beam with wavelenth= 1 X 10-10m and a gamma-ray beam from a Cs137 sample with wavelength= 1.88 X 10-12m. If the radiation scattered form free electron is viewed at 90 deg to the incident beam
a) What is the Compton wavelength shift in each case?
b) What kinetic energy is given to a recoiling electron in each case?
c) What percentage of the incident photon energy is lost in each case?

Homework Equations

The Attempt at a Solution

 

[jennyhelp]

An radioactive gamma source produces an electron positron pair in an absorber. The electron/positron pair produce tracks in a drift chamber that has a field of 0.2 weber/m2. The radius of the drift is 2.5 X 10-2m. Using the equation for momentum of a particle given a bending radius of curvature of a particle in a magnetic field:
p = eBr
where p is the momentum, e is the electronic charge, B is the magnetic field (in MKS units) and r is the radius of curvature, find the energy and wavelength of the pair-producing photon.

 

[jennyhelp]

The term ‘cross section’ is a physicists term that we will be using throughout the quarter to describe the interaction of radiation with matter. This term comes from the notion that when particles interact, the strength of their interaction can be represented by the collision of two hard spheres with the radius of the ‘cross section’. The cross section is defined for one particle, and thus when a particle strikes an absorber, the cross section is multiplied by the number density of the absorber. So…the absorption coefficient is then defined as:
L = 1/ n*sigma,
Where n is the L is the absorption coefficient, n is the number density, and sigma is the cross section for the interaction. Knowing this, the fact that the cross section removes particles from a beam (Beer’s law) (and any other facts you can get from your modern physics text: you may have to use dimensional analysis):
A beam of neutrons of kinetic energy 0.29 eV, intensity 105 /s traverses an absorber of 92U235 of mass thickness 10-1 kg/m2. The collision can result in the following events:
a) Elastic, billiard ball scattering Sigmaf = 2 X 10-30 m2
b) Capture of the neutron followed by emission of a gamma-ray Sigmae = 7 X 10-27 m2
c) Capture of the neutron followed by nuclear fission f = 2 X 10-26 m2
Calculate:
a) Attenuation of the neutron beam by the absorber
b) Number of fission reactions occurring per second
c) The flux of elastically scattered neutrons at a point 10 m from the absorber and out of the main beam, assuming that the elastic scattering is isotropic.

 

[jennyhelp]

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[jennyhelp]

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[skanda9051]

1) The wave length of scattered photon of x ray is 1.02x10-10m

2) the wave length of scattered photon of gama ray is 4.306x10pico meter

3) KE of scattered electron of x ray photon is 1.987x10+12

4)KE of scattered electron of gama ray photon is 5.96x10+10

5)the loss of energy in case of x ray is 2%

6)the loss of energy in case of gama ray is 43.6%