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Chapter 30: Problem 10

In the Cornell Electron Storage Ring, electrons and positrons circulate in opposite directions with kinetic energies of 6.0 GeV each. When an electron collides with a positron and the two annihilate, one possible (though unlikely) outcome is the production of one or more proton-antiproton pairs. What is the maximum possible number of proton-antiproton pairs that could be formed?

Short Answer

Expert verified
Answer: To find the maximum number of proton-antiproton pairs that could be formed, follow these steps: 1. Calculate the total energy available for the collision by adding the kinetic energies and rest energies of the electron and positron. 2. Calculate the energy required to create one proton-antiproton pair using the rest energy of a proton and antiproton. 3. Divide the total energy available for the collision by the energy required to create one proton-antiproton pair. After completing these steps, you will find the maximum possible number of proton-antiproton pairs that can be formed during the collision.

Step by step solution

01

Find the total energy available for the collision

We are given the kinetic energy of the electron and positron as 6.0 GeV each. To find the total energy available for the collision, we must also take into account their rest energies. The rest energy of an electron (E_e) or a positron (E_p) can be calculated using the formula E=mc^2, where m is the mass of the particle, and c is the speed of light. The mass of an electron, positron, and proton is given as: m_e = m_p = 9.11*10^{-31} kg and m_proton=1.67*10^{-27} kg. The rest energies of the electron and positron are the same and they are \[E_e = E_p =(m_e c^2) = (9.11*10^{-31} kg)*(3 * 10^8 m/s)^2\] Now we need to calculate the total energy available for the collision. The energy of an electron and positron are added: \(TotalEnergy_{collision} = (E_e + 6.0GeV) + (E_p + 6.0GeV)\)
02

Find the energy required to create one proton-antiproton pair

To calculate the energy required to create one proton-antiproton pair, we need to find the rest energy of one pair using the formula E=mc^2, where m is the mass of the pair and c is the speed of light. The mass of a proton is given as m_proton=1.67*10^{-27} kg. The mass of an antiproton is the same as the mass of a proton. Therefore, the energy required for one proton-antiproton pair (E_pair) is: \[E_{pair} = 2*(m_{proton} c^2) = 2*(1.67*10^{-27} kg)*(3 * 10^8 m/s)^2\]
03

Calculate the maximum number of proton-antiproton pairs that could be formed

To find the maximum possible number of proton-antiproton pairs that could be formed, we need to divide the total energy available for the collision by the energy required to create one proton-antiproton pair. Let's denote the maximum number of pairs as N_max. \(N_{max} = \frac{TotalEnergy_{collision}}{E_{pair}}\) By calculating the ratio of TotalEnergy_{collision} and E_{pair}, we can find the maximum possible number of proton-antiproton pairs that can be formed during the collision.

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Most popular questions from this chapter

A neutral pion (mass \(0.135 \mathrm{GeV} / \mathrm{c}^{2}\) ) decays via the electromagnetic interaction into two photons: $\pi^{0} \rightarrow \gamma+\gamma$ What is the energy of each photon, assuming the pion was at rest?
A sigma baryon at rest decays into a lambda baryon and a photon: $\Sigma^{0} \rightarrow \Lambda^{0}+\gamma .$ The rest energies of the baryons are given by \(\Sigma^{0}=1192 \mathrm{MeV}\) and \(\Lambda^{0}=1116 \mathrm{MeV} .\) What is the photon wavelength? [Hint: Use relativistic formulas and be sure momentum is conserved as well as energy.]
A proton of mass \(0.938 \mathrm{GeV} / c^{2}\) and an antiproton, at rest relative to an observer, annihilate each other as described by \(\mathrm{p}+\overline{\mathrm{p}} \rightarrow \pi^{-}+\pi^{+} .\) What are the kinetic energies of the two pions, each of which has mass $0.14 \mathrm{GeV} / \mathrm{c}^{2} ?$
When a proton and an antiproton annihilate, the annihilation products are usually pions. (a) Suppose three pions are produced. What combination(s) of \(\pi^{+}, \pi^{-},\) and \(\pi^{0}\) are possible? (b) Suppose five pions are produced. What combination(s) of \(\pi^{+}, \pi^{-},\) and \(\pi^{0}\) are possible? (c) What is the maximum number of pions that could be produced if the kinetic energies of the proton and antiproton are negligibly small? The mass of a charged pion is \(0.140 \mathrm{GeV} / c^{2}\) and the mass of a neutral pion is \(0.135 \mathrm{GeV} / c^{2}.\)
Show that the charge of the neutron and the charge of the proton can be derived from their constituent quark content.
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