A 110-keV X-ray photon coherently scatters off one of the valence electrons of a
ID: 1263976 • Letter: A
Question
A 110-keV X-ray photon coherently scatters off one of the valence electrons of a nitrogen atom. Assume that the scattering angle of the photon is
? = 12
A 110-keV X-ray photon coherently scatters off one of the valence electrons of a nitrogen atom. Assume that the scattering angle of the photon is ? = 12degree. (Use 511 keV for the energy of an electron at rest, 1.602 x10-19 C for the charge of the electron, and 2.998 x10^8 m/s for the speed of light in vacuum.) (d) By what angle would the photon have to be scattered in order for its energy to be reduced by 13%? Derive the result as a general formula first, then calculate the particular angle for an incident photon of 110 keV.Explanation / Answer
The Compton effect is the elastic scattering of photons from electrons. As a reaction, the process is:
? + e ? ? ? + e ? .
Since this is a two body elastic scattering process, the angle of the scattered photon is completely correlated with the energy of the scattered photon by energy and momentum conservation.
This relation is usually written as: ?? = ? 0 ? ? = h /mc (1 ? cos ?) (1) where ? and ? 0 are the wavelengths of the incident and scattered photon respectively, and ? is the photon scattering angle.
The energy of a photon is related to its frequency and wavelength as:
E = h? = hc/? (2) where c is the velocity of light. Combining Eq. (1) and (2) the energy of the scattered photon is: E
E 0 = E /1 + E /mc2 (1 ? cos ?)
The kinetic energy of the recoil electron is:
Te = E ? E 0 = E ?(1 ? cos ?) /1 + ?(1 ? cos ?)
where ? = h?/mc2
above concept is sufficient to answer
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.