An X-ray source of unknown wavelength is directed at a carbon sample. An electron is scattered with a speed of 4.5x107m/s at an angle of 60°. Determine the wavelength of the X-ray source.

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You can solve these sort of problems using four-momentum algebra. In c = 1 units, the four momentum of a particle, Pf, is:

Pf = (E, P)

E is the energy and P is the momentum. P has 3 components so Pf has four components. Pf transforms as a four-vector under Lorentz transformations. The inner product of two four momenta:

Pf1 = (E1, P1)

Pf2 = (E2, P2)

is defined as:

Pf1 dot Pf2 = E1 E2 - P1 dot P2

where P1 dot P2 is the ordinary inner product of the ordinary momenta P1 and P2.

This inner product is invariant under Lorentz transformations. We denote the inner product of a four-vector Pf with itself as Pf^2. Also ordinary inner products of ordinary vectors with themselves are denoted as a square. Let's take a closer look at the square of a general four-momentum

Pf^2 = E^2 - P^2

This is invariant under Lorentz transformations i.e. it's value is the same in all frames. If we ...

Solution Summary

The solution is derived from first principles using four-momentum algebra.

An X-ray photon of wavelength 6 pm (1 pm = 10^-12 m) makes a head-on collision with an electron, so that the scattered photon goes in a direction opposite to that of the incident photon. The electron is initially at rest.
(a) How much longer is the wavelength of the scattered photon than that of the incident photon?
(b) W

1. A 100-keV x ray is Compton-scattered through an angle of 90 degrees. What is the energy of the x ray after scattering?
a. 83.6 keV
b. 121 keV
c. 114.5 keV
d. 100 keV
2. What is the de Broglie wavelength of a particle moving at a speed of 1.00 x 10^6 m/s if it is (a) an electron (b) a proton? (me= 9.11

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a) What wavelength would be needed to vie a maximum speed of 4.81 x 10^5 m/s?
b) Can you guess what metal it is?
Problem 2. In positron emission tomography an electron and positron annihilate,

Consider the 2.0micrometer long GaAs device where the E-field is 5kV/cm and Mn*=.067M0.
(a) Calculate the transit time of an electron through the device if the mobility is 8000 cm^2V-s.
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Sketch the sixth-order Feynman diagram representing Delbruck scattering:
r + r -> r+ r. (This process, the scattering of light by light, has no analog in classical electrodynamics.)
This question is from the textbook 'Introduction to elementary particles' by David Griffiths.

This solution describes the basics of an x-ray tube for medical and basic-science applications. Through multiple choice questions, the principle of the acceleration of electrons onto a high-Z target for x-ray production is discussed. Some details about the underlying physics for generating Bremstrahlung and line-emission x-rays