What Is the Mass-Energy Ratio in Proton-Antiproton Annihilation?

[humsafar]

Homework Statement

I just want to calculate the mass-energy ratio of annihilation of proton and antiproton and compare it with the observed result, e.g the mass of the two particles before annihilation and energy calculated and observed both after annihilation...I need a detailed and descriptive answer...

Homework Equations

E=MC^2 ?

The Attempt at a Solution

proton and anti-proton may release 2 x 0.938 GeV/c2 in energy in the form of new particles. 0.938 GeV/c2 being rest mass of a proton...but i am not sure...

 

[mark726]

Dear student,

Thank you for your question. The mass-energy ratio of annihilation of a proton and antiproton can be calculated using Einstein's famous equation, E=mc^2. In this case, we will be using the rest mass of the proton, which is approximately 0.938 GeV/c^2.

First, let's define what we mean by annihilation. When a proton and antiproton come into contact, they can annihilate each other, resulting in the production of new particles. This process is known as pair annihilation. The new particles that are produced are typically two photons, each with an energy of 0.938 GeV. This is because the total energy before and after annihilation must be conserved.

Now, let's look at the mass-energy ratio of this process. We can calculate the total energy of the proton and antiproton before annihilation by simply adding their rest masses together. This gives us a total initial energy of 2 x 0.938 GeV/c^2 = 1.876 GeV/c^2.

After annihilation, we have two photons, each with an energy of 0.938 GeV. The total energy after annihilation is therefore 2 x 0.938 GeV = 1.876 GeV.

To calculate the mass-energy ratio, we simply divide the total energy after annihilation by the total initial energy. In this case, we get a ratio of 1.876 GeV / 1.876 GeV = 1. This means that the mass-energy ratio of annihilation of a proton and antiproton is exactly 1, which is in agreement with what we would expect from Einstein's equation.

In terms of comparing this calculated result with the observed result, we would need to look at the experimental data for pair annihilation of protons and antiprotons. This data can vary depending on the specific experimental setup and conditions, but it should be close to the calculated value of 1.

I hope this explanation helps you better understand the mass-energy ratio of annihilation of a proton and antiproton. If you have any further questions, please don't hesitate to ask. Good luck with your studies!