Let\'s presume that the goal is to collide two protons as calculated in the lect

Question

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 4.0 times that of a proton, so its rest energy is Em(X)=4.0 Mp c^2. Note that as in lecture, teh 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 2 Mp c2 -worth of kinetic energy left over so the X's can move once they are produced?

Explanation / Answer

The rest energy of each proton is E =1Mpc2

The rest energy of newparticle is Ex =4Mpc2

The additional rest energy required to produce a particle X at rest is 3Mpc2

The kinetic energy 1Mpc2 is also required for each particle.

Therefore the additional energy required for each proton is 4Mpc2

Then each new particle X = 4Mpc2 will move with kinetic energy of 1Mpc2

NOTE : EACH "MOVING" PARTICLE WILL HAVE A TOATAL ENERGY OF 5Mpc2

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