How much energy is required to produce the electron-positron pair

In summary, the total energy required to produce an electron-positron pair in the field of a nucleus (with Z=20) is 10.88keV. This is calculated by adding the energy of the captured electron in the ground 1s state, which is -5442eV, to the energy of the created positron, which is assumed to be the same as the electron's energy. The field of the nucleus does not significantly affect the needed energy, and it is unclear why it was mentioned in the original question.
  • #1
vst98
51
0

Homework Statement


How much energy is required to produce the electron-positron pair in the filed of nucleus (Z=20) if electron is captured to the ground 1s state of the system.

The Attempt at a Solution



I can calculate the energy of the captured electron from

E = - εZ2/(2n2) where ε=me4/hbar2≈27.2eV

E = - 5442eV

Now I have to add this energy to the energy of created positron to have total required energy, right ? But I do not know how to find energy of a positron.
 
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  • #2
hi vst9! :smile:
vst98 said:
… But I do not know how to find energy of a positron.

won't it be the same as the energy of the electron?
 
  • #3
hi tiny-tim !

Yes I think so, then it is the energy and momentum conservation that places a restriction
on the positron to have the same energy as electron , right ?

I was a little bit confused by the "... in the filed of nucleus" part of the question, then
this filed of a nucleus does not change much (except maybe the needed energy).

So, the needed energy for pair creation is E=2*5442=10.88keV
 
  • #4
hi vst98! :wink:

right! :smile:

i'm not sure why they mentioned the field (not "filed" :wink:) … it doesn't seem to add anything to the rest of the question :confused:
 
  • #5
Ok, thanks !

(yes it is "field" and not "filed" in the original question, my flip error :) )
 

1. What is an electron-positron pair?

An electron-positron pair is a pair of particles that have the same mass as each other, but opposite charges. The electron has a negative charge, while the positron has a positive charge.

2. How is an electron-positron pair produced?

An electron-positron pair can be produced through various processes, such as particle collisions or radioactive decay. In particle colliders, high-energy particles are accelerated and then collide, producing an electron-positron pair as a result of the collision. In radioactive decay, a nucleus decays into an electron-positron pair.

3. How much energy is required to produce an electron-positron pair?

The energy required to produce an electron-positron pair depends on the process used to create it. In general, the minimum energy required is twice the rest mass energy of an electron (1.02 MeV) and a positron (also 1.02 MeV), which is 2.04 MeV.

4. Can an electron-positron pair be produced in a vacuum?

Yes, an electron-positron pair can be produced in a vacuum. In fact, electron-positron pairs are constantly being produced and annihilated in the vacuum due to the quantum fluctuations of energy. However, in order for a pair to be produced and remain stable, a certain amount of energy is required.

5. What happens to an electron-positron pair after it is produced?

An electron-positron pair can either annihilate each other, producing two high-energy photons, or they can exist separately as individual particles. The fate of the pair depends on the energy and conditions of the environment in which they were produced.

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