MCQ The phenomenon of pair production is energy conversion to
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The photoelectric and Compton effects represent two mechanisms of photon absorption, the process in which a photon gives up some or all of its energy to a material particle (contained usually within an atom in a solid). Photon absorption can be quantified in terms of an absorption coefficientm ,commonly expressed in units of m^-1 or cm^-1 and defined by the eq uation:
I(x) = I(0) exp(-(mu) x)
where I(0) and I(x) are the photon intensities (W/m^2) at the entrancesurface and at a depth x below the surface (measured in the direction of the incident beam). The intensity therefore decays exponentially within the material, as shown in Fig. 4-26. We can also take x as being the entire thickness of the material, in which case I(x) represents the photon intensity at the exit surface. By placing radiation detectors in front and behind a sheet of material of known thickness x, the absorption coefficient can be measured.
If the experimentally determined (mu) is plotted as a function of increasing photon frequency f (or photon energy hf), its value falls continuously within the visible, ultraviolet and x-ray regions but eventually reaches a minimum and then starts to increase in the g -ray region; see Weidner & Sells Fig. 4.24. The reason for the initial decrease is that the absorption processes of photoelectric and Compton scattering become less probable as the photon energy increases; in other words, higher-energy radiation is more penetrating.
The eventual rise in (mu) indicates that a third process occurs at high photon energy; this is pair production, in which a pair of elementary particles (a particle and its antiparticle of the same mass but opposite electrostatic charge) are created from the energy (hf) of the original photon. In this case, the two particles are an electron and an antielectron (more commonly known as a positron, whose rest mass m0 is the same as that of an electron but whose charge is +e ).
Pair production can be represented by an equation which represents the conservation of total energy (or mass-energy):
hf = 2(m0 c^2) + K(-e) + K(+e)
Here, (m0 c^2) = 0.511 MeV is the rest energy of an electron, which is equal to that of the positron, so the factor of 2 represents the fact that two particles of identical rest mass are created. K(-e) and K(+e) represent the kinetic energy of the electron and positron, immediately after their creation.
If the photon energy were exactly 2m0 c^2 = 1.02 MeV, the two particles would be created at rest (with zero kinetic energy) and this would be an example of the complete conversion of energy into mass. For photon energies below 2m0c^2, the process cannot occur; in other words, 1.02 MeV is the threshold energy for pair production. For photon energies above the threshold, a photon has more than enough energy to create a particle pair and the surplus energy appears as kinetic energy of the two particles.
There is, however, a further condition which must be satisfied during the pair-production process: conservation of momentum. Taking this requirement into account, we can anticipate that pair production cannot take place in empty space; something must absorb the momentum (p=h/l =hf/c) of the initial photon. (To see this, consider the threshold situation where the particles have to be created at restand cannot themselves absorb anymomentum). The photon momentum can be absorbed by an atomic nucleus, which is thousands of times more massive than an electron or positron and can therefore absorb momentum without absorbing much energy; therefore the energy-conservation equation above remains approximately valid. Consequently, pair production is observed when high-energy gamma rays enter a solid, where a high density of atomic nuclei is present.
There exists an inverse process to pair production called pair annihilation, in which a particle and its antiparticle collide and annihilate each other, the total energy of the two particles appearing as electromagnetic radiation. In the case of an electron and positron, the energy balance can be represented as:
2m0c^2 + K(-e) + K(+e) = 2 hf
.
I(x) = I(0) exp(-(mu) x)
where I(0) and I(x) are the photon intensities (W/m^2) at the entrancesurface and at a depth x below the surface (measured in the direction of the incident beam). The intensity therefore decays exponentially within the material, as shown in Fig. 4-26. We can also take x as being the entire thickness of the material, in which case I(x) represents the photon intensity at the exit surface. By placing radiation detectors in front and behind a sheet of material of known thickness x, the absorption coefficient can be measured.
If the experimentally determined (mu) is plotted as a function of increasing photon frequency f (or photon energy hf), its value falls continuously within the visible, ultraviolet and x-ray regions but eventually reaches a minimum and then starts to increase in the g -ray region; see Weidner & Sells Fig. 4.24. The reason for the initial decrease is that the absorption processes of photoelectric and Compton scattering become less probable as the photon energy increases; in other words, higher-energy radiation is more penetrating.
The eventual rise in (mu) indicates that a third process occurs at high photon energy; this is pair production, in which a pair of elementary particles (a particle and its antiparticle of the same mass but opposite electrostatic charge) are created from the energy (hf) of the original photon. In this case, the two particles are an electron and an antielectron (more commonly known as a positron, whose rest mass m0 is the same as that of an electron but whose charge is +e ).
Pair production can be represented by an equation which represents the conservation of total energy (or mass-energy):
hf = 2(m0 c^2) + K(-e) + K(+e)
Here, (m0 c^2) = 0.511 MeV is the rest energy of an electron, which is equal to that of the positron, so the factor of 2 represents the fact that two particles of identical rest mass are created. K(-e) and K(+e) represent the kinetic energy of the electron and positron, immediately after their creation.
If the photon energy were exactly 2m0 c^2 = 1.02 MeV, the two particles would be created at rest (with zero kinetic energy) and this would be an example of the complete conversion of energy into mass. For photon energies below 2m0c^2, the process cannot occur; in other words, 1.02 MeV is the threshold energy for pair production. For photon energies above the threshold, a photon has more than enough energy to create a particle pair and the surplus energy appears as kinetic energy of the two particles.
There is, however, a further condition which must be satisfied during the pair-production process: conservation of momentum. Taking this requirement into account, we can anticipate that pair production cannot take place in empty space; something must absorb the momentum (p=h/l =hf/c) of the initial photon. (To see this, consider the threshold situation where the particles have to be created at restand cannot themselves absorb anymomentum). The photon momentum can be absorbed by an atomic nucleus, which is thousands of times more massive than an electron or positron and can therefore absorb momentum without absorbing much energy; therefore the energy-conservation equation above remains approximately valid. Consequently, pair production is observed when high-energy gamma rays enter a solid, where a high density of atomic nuclei is present.
There exists an inverse process to pair production called pair annihilation, in which a particle and its antiparticle collide and annihilate each other, the total energy of the two particles appearing as electromagnetic radiation. In the case of an electron and positron, the energy balance can be represented as:
2m0c^2 + K(-e) + K(+e) = 2 hf
.
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