Concept explainers
(a)
The minimum photon energy required to produce a proton-antiproton pair from collision of photon with a free electron at rest.
(a)
Answer to Problem 55P
The minimum required energy for production of electron-positron pair is
Explanation of Solution
Write the expression for the energy of the electron-positron pair in inertial frame.
Here,
The rest energy for an electron is
Write the expression for the initial energy of the electron-positron pair using conservation of energy.
Substitute
Here,
Write the expression for the energy of the electron in the relativistic frame of reference.
Here,
Write the expression for the Doppler’s shift in the energy of the photon in laboratory frame.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the minimum required energy for production of electron-positron pair is
(b)
The minimum photon energy required to produce a proton-antiproton pair from collision of photon with a free proton at rest.
(b)
Answer to Problem 55P
The required minimum energy from a proton at rest is
Explanation of Solution
Write the expression for the proton’s rest energy.
Here,
Write the expression for the energy of the electron-positron pair in inertial frame.
Write the expression for the conservation of the energy for the photon.
Substitute
The value of rest energy of the electron is
So, the energy of the proton is
Conclusion:
Substitute
Therefore, the minimum energy required from the rest photon is
Substitute
Thus, the required minimum energy from a proton at rest is
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Chapter 3 Solutions
Modern Physics for Scientists and Engineers
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