PLEASE CHANGE THE NUMBERS USED IN THIS QUESTION. Instead of 9.0, use 8.0 for bot

Question

PLEASE CHANGE THE NUMBERS USED IN THIS QUESTION. Instead of 9.0, use 8.0 for both times the number is used. and instead of 4.5 use 4.

Let's presume that the goal is to collide two protons as calculated in the lecture in order to produce two new particles called "X." Each X has a mass of 9.0 times that of a proton, so its rest energy is E_m(X) = 9.0 M_p c^2. Note that as in lecture, the scale of energies is in units of the rest energy of the proton. How much kinetic energy should each beam have in units of the rest energy of the protons in order to not only produce two X's, but also to have a total of 4.5 M_p c^2 -worth of kinetic energy left over so the X's can move once they are produced? M_p c^2

Explanation / Answer

The rest energy of each proton is

E = mp c^2

the rest energy of new particle is

E' = 9.0 mp c^2

the kinetic energy required for each particle is

E'' = 4.5 mp c^2/2 = 2.25 mp c^2

the total energy of each moving particle is

E total = E' + E'' = 9.0 mp c^2 + 2.25 mp c^2 = 11.25 mp c^2

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