Chapter 6: Q14E (page 1520)

Calculate the minimum beam energy in a proton-proton collider to initiate the $p + p \to p + p + η$ ⁰ reaction. The rest energy of the $η °$ is $547.3 M e V .$

Short Answer

Expert verified

The minimum beam energy in a proton-proton collider to initiate the $p + p \to p + p + η^{0}$ reaction is $E_{m} = 1212 M e V .$

Step by step solution

Definition of Law of conservation of energy

It states that total energy of a system is constant. It can change from one type of energy to another but never completely lost. System and enviroment interacts and exchange energy if the system allows.

Determine The minimum beam energy in a proton-proton collider to initiate the p+p→p+p+η0 reaction

The minimum available energy is:

$E_{α} = m_{p} c^{2} + m_{p} c^{2} + m_{η} c^{2}$

Put known values, the rest energy of the proton is $938.3 M e V$ , and the rest energy of $η °$ is $547.3 M e V$

So,

$E_{α} = 938.3 M e V + 938 M e V + 547.3 M e V E_{α} = 2423.9 M e V$

The total energy equals half the available energy in colliding beams

$E_{m} = E_{α} / 2 E_{m} = (2423.9 M e V) / 2 E_{m} = 1211.95 M e V E_{m} = 1212 M e V$

Hence, the minimum beam energy in a proton-proton collider to initiate the

$p + p \to p + p + η^{0}$ reaction is $E_{m} = 1212 M e V .$

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Calculate the minimum beam energy in a proton-proton collider to initiate the $p + p \to p + p + η$ ⁰ reaction. The rest energy of the $η °$ is $547.3 M e V .$

Short Answer

Step by step solution

Definition of Law of conservation of energy

Determine The minimum beam energy in a proton-proton collider to initiate the p+p→p+p+η0 reaction

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Calculate the minimum beam energy in a proton-proton collider to initiate the p+p→p+p+η0 reaction. The rest energy of the η° is 547.3 MeV.

Short Answer

Step by step solution

Definition of Law of conservation of energy

Determine The minimum beam energy in a proton-proton collider to initiate the p+p→p+p+η0 reaction

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Oscillations

Thermodynamics

Fluids

Mechanics and Materials

Fields in Physics

Study anywhere. Anytime. Across all devices.

Calculate the minimum beam energy in a proton-proton collider to initiate the $p + p \to p + p + η$ ⁰ reaction. The rest energy of the $η °$ is $547.3 M e V .$