1) Last year a proposal was made to use a proton accelerator and a separate electron accelerator to collide head-on 9 GeV protons with 7.8 GeV electrons in the proposed Electron-ion collider in China (EicC). (a) Use four-vectors to deduce an expression for the centre-of-mass energy which would be produced in each e-p collision. [5 marks] (b) Use your expression from part (a) to calculate the centre-of-mass energy for the e-p system. [2 marks] Instead of a proton beam, suppose that stationary protons will be used as the target. Calculate the electron beam energy required to obtain the same centre- of-mass energy in part (b). [5 marks] (d) If the electron beam energy is 75 GeV calculate the distance probed inside the proton. [3 marks]