Energy transferred to nucleus in pair-production

In summary, the conversation discusses the role of the nucleus in absorbing energy and momentum during a reaction. There is a question about the maximum kinetic energy of a sodium atom and whether it takes into account nuclear excitation. The conversation concludes that there is not enough information to determine the maximum energy.
  • #1
a1234
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Homework Statement
Gamma rays of 22 MeV interact with a sodium sample, resulting in a pair-production reaction, in which an electron and positron are created in the vicinity of a nucleus:
(Photon + nucleus = e- + e+ + nucleus)
What would be the maximum transfer of energy to the sodium atoms in this reaction?
Relevant Equations
E_gamma = 2m_e*c^2 + KE- + KE+ + K_nucleus
In most textbooks, the recoil energy of the nucleus is ignored as it absorbs so little energy, and since its main role in the reaction is to absorb some of the photon's momentum without absorbing much energy.
I'm tempted to say that the nucleus gets the maximum energy when the kinetic energy of the electron and positron are zero, but I don't think we'd ever see an atom with a kinetic energy of 20.978 MeV. Wouldn't some of that energy go towards nuclear excitation?
 
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  • #2
Are you sure you are not over-thinking this?
 
  • #3
I feel like I am. I've been staring at the energy and momentum conservation equations to try to find something more "sophisticated," but that doesn't seem to work out since we don't have enough information (e.g. the scattering angle or velocities of the electron-positron pair).
 
  • #4
a1234 said:
I feel like I am. I've been staring at the energy and momentum conservation equations to try to find something more "sophisticated," but that doesn't seem to work out since we don't have enough information (e.g. the scattering angle or velocities of the electron-positron pair).
You're trying to find the maximum (kinetic) energy of the sodium atom. You've already established the criteria for that.
 
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Related to Energy transferred to nucleus in pair-production

1. What is pair-production?

Pair-production is a process in which a gamma ray photon is converted into an electron and a positron (the anti-particle of an electron) in the presence of a nucleus.

2. How is energy transferred to the nucleus in pair-production?

The energy transferred to the nucleus in pair-production is equal to the energy of the original gamma ray photon minus the rest mass energy of the electron and positron pair. This energy is transferred through the interaction between the photon and the nucleus.

3. What is the role of the nucleus in pair-production?

The nucleus plays a crucial role in pair-production as it provides the necessary energy for the conversion of a gamma ray photon into an electron and a positron. The nucleus also helps to conserve momentum during the process.

4. Can pair-production occur without the presence of a nucleus?

No, pair-production cannot occur without the presence of a nucleus. The energy of the gamma ray photon must be transferred to a nucleus in order for the process to take place.

5. What are the applications of pair-production in scientific research?

Pair-production has many applications in scientific research, including the production of positron emission tomography (PET) scans, the study of high-energy particle collisions, and the creation of anti-matter for further study. It also plays a role in understanding the behavior of matter and energy in extreme conditions, such as in the early universe or in the vicinity of black holes.

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