Lets presume that the goal is to collide two protons as calc

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 3.0 times that of a proton, so its rest energy is Em(X)=3.0 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 1.5 Mp c2 -worth of kinetic energy left over so the X\'s can move once they are produced?

Solution

Rest mass energy of X = 3.0m_p c²

Kinetic energy of X       = 1.5m_p c²

According to the relativity, K.E = mc² - rest mass energy

i.e., 1.5m_p c² = 2mc² - 3.0m_p c²

2mc² = 4.5m_p c²

Since two prortons are combined to form X, the energy should be 2mc² .

Therefore energy of each beam is, mc² = 4.5m_p c² / 2 = 2.25 m_p c² .