تأثير كومبتون ComptonEffect
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Arthur H. Compton observed the scattering of xraysfrom electrons in a carbon target and found scattered xrays with a longer wavelength than those incident upon the target. The shift of the wavelength increased with scattering angle according to the Compton formula: Compton explained and modeled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength according to the Planck relationship.

At a time (early 1920's) when the particle (photon) nature of light suggested by thephotoelectric effect was still being debated, the Compton experiment gave clear and independent evidence of particlelike behavior. Compton was awarded the Nobel Prize in 1927 for the "discovery of the effect named after him".
Compton Scattering Experiment.
Theoretical Analysis of Compton's Experimental Observations
Compton used the Einstein’s concept of photon for the first time in the analysis of the observations in his experiments. A photon is a localized packet of energy. It may be considered as a particle of energy E_{0} given by Planck's quantum hypothesis E_{0}= hν and momentum p_{0} given by De Broglie relation p_{0} = h / λ where ν is the frequency and λ is the wavelength of the X ray photon.
The wavelength of the X ray photons is ≤1A^{0} and energy hν≥ 10^{4} eV. Due to the high energy of the photons, the velocity acquired by the electrons is very high and comparable to the speed of light. Hence it is necessary to use relativistic expressions for the kinetic energy and momentum of the electrons.
The general equation for the total relativistic energy E in terms of rest mass m_{0} is given by
Velocity of the photon is c, its energy E_{0} = hν is finite. Hence the rest mass of photon must be zero. Its energy is entirely kinetic, Momentum p_{0} of the photon is obtained from the general equation
Momentum of photon p_{0} is given by p_{0} = h / λ
The interaction between incident Xray photon and an electron in the target may be considered as a collision between two particles. Compared to the energy of the Xray photons, the binding energy of the electrons in the target material is small and they may be treated as free electrons. Xray Photon having total relativistic energy E_{0} and momentum p_{0} strikes a stationary electron having mass me and rest mass energy m_{e}c^{2}. The incoming photon gives part of its energy to one of the loosely bound (almostfree electrons) in the outer shell of the atom or molecule in the stationary target This energy of photon is used to release and give kinetic energy to the electrons. After the collision the ejected electron recoils with kinetic energy T_{2} and momentum p_{2} in the direction making an angle ф. Its total energy E_{2}is the sum of kinetic energy T_{2} and rest mass energy m_{e}c^{2}. Xray photon is scattered with the remaining total relativistic energy E_{1} and momentum p1in a direction making an angle θ with the original direction, This interaction is according to the conservation of linear momentum and total energy in inelastic scattering. As some energy of the scattered X ray photons is lost (to the recoiling electron), the frequency ν of the scattered Xray photon is decreased to ν’or its wavelength λ is increased to λ’. It is calculated using the relations as follows
According to the conservation of momentum
Φ is eliminated by squaring and adding above two equations
According to the conservation of total relativistic energy
E_{0} + m_{e}c^{2} = E_{1} + T_{2} + m_{e}c^{2}
E_{0} − E_{1} = T_{2}
hv − hv' = T_{2}
However
c(p_{0} − p_{1}) = T_{2}
Energy of the electron after collision is given by
E_{2} = T_{2} + m_{e}c^{2}
E_{2} is also expressed by
where the general equation E^{2} = c^{2}p^{2} + (m_{0}c^{2})^{2} is applied to the electron
Equating the above two expressions for energy of the electron
m_{e}c(p_{0} − p_{1}) = (p_{0}p_{1})(1 − cosθ)
Using algebraic relations to eliminate variables Compton arrived at the following relationship between the shift in wavelength and the scattering angle θ in terms of constant parameters as follows
is the initial wavelength of the Xray photon
is the wavelength after scattering of the Xray photon
is the Compton wavelength
h is the Planck constant
m_{e} is the mass of the electron
c is the speed of light
θ is the scattering angle of the Xray photon.
It is known as the Compton equation. From the formula, theoretical value of the wavelength for scattering at θ = 90^{0} comes out to be 0.0733 nm. It is consistent with the experimental value 0.0731 nm (refer to the table)
Compton Shift
The quantity is called as the Compton wavelength of the electron. Its value is equal to 2.43×10^{ − 12} m.
The wavelength shift is called as the Compton Shift.
The Compton Shift varies with the scattering angle of photon as follows
It has Minimum value Δλ = zero (for θ = 0°)
when the incident photon is not deflected from its path
It is called as a “Grazing collision” of photon with electron
It has Maximum value = Twice the Compton wavelength (for θ= 180°).
When the incident photon reverses its direction
It is called as a “Headon collision” of photon with electron
From the graphs it is seen that in addition to the shifted wavelength an unmodified wavelength also is present. It is due to the scattering of Xray photon from tightly bound electrons. In that case, not a single loose or free electron but the entire atom is involved in the interaction with photon and it recoils. In the formula for mass of atom M_{A} (instead of mass of electronm_{e}) is to be used. M_{A} > > m_{e}. Hence, is a minute, almost negligible quantity i.e. wavelength remains unaffected after scattering.
Similar reasoning applies if light photons in the visible range are used. They have longer wavelengths of the order of 500 nm. Their energies are far too smaller than Xrays and not sufficient to overcome the binding energies of even the loosely bound electrons. The wavelength shift is very very small in comparison to their wavelength. By using them it is difficult to detect minute wavelength shift .On the contrary, Xrays have short wavelengths of the order of 0.1 nm. Their use makes the measurement of minute wavelength shift (of less than 0.1 nm) comparatively easy. Hence X ray photons were found to be more appropriate to demonstrate the scattering between photons and electrons and confirm the particle nature of light.
1.4.3 The Compton Effect
Compton scattering is a type of inelastic scattering that high energy Xrays, gamma rays undergo in matter. When a X ray or gamma ray photon collides with an electron in matter, part of its energy is transferred to the electron, which recoils and is ejected from its atom (atom becomes ionized). X ray or gamma ray is scattered with the remaining energy. Due to the "degradation" or a decrease in energy, its wavelength is increased. It is called as the Compton effect.
The relationship between the shift in wavelength and the scattering angle θ, called as the Compton shift is given by
The Compton shift depends upon the angle of scattering θ,. Wavelength λ’ of the scattered X ray photon depends upon the angle of scattering θ and also the mass of the recoiling electron
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