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In the ultra-relativistic case the momentum of a particle accelerated by a potential difference varphi is found with the aid of the formula p= evarphi//c, this value being expressed in units of MeV//c, where c is the velocity of light in a vacuum. Express this unit in the SI system. Find out for what poten tial differences the use of this formula leads to an error of less than 5%. Do the calculations both for the electron and the proton. |
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Answer» Solution :The relative error is `EPSILON= (p_("rel")-evarphi//c)/(p_("rel"))= 1-sqrt((evarphi)/(2E_(0)+evarphi))` hence `varphi= (2E_(0))/(E).((1-e)^(2))/(2epsilon-epsilon^(2))= (E_(0))/(epsilone)` |
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