You will need a calculator with lots of digits for some parts of this problem. At the Large Hadron Collider at the CERN laboratory in Geneva, Switzerland, protons (with mass of 0.938 GeV/c²) moving in opposite directions are accelerated to energies of 6.5 TeV and then smashed into each other.

relativistic ? factor for these protons= 3732.34

14). What fraction of the speed of light are the protons moving? (From y = 1/ \\/ [1- (v/c)2] one can derive the expression We = \\/ (1-1/y2) ). Include enough decimal places so that you have one digit which does not equal to 9. Depending on your calculator, you may have to use sqrt(1-1/gamma"2) = 1- 1/(2*gamma'\\2). You may also have to use a value of gamma a factor of 10 or 100 smaller than it really is and then do the subtraction from 1 by hand after adding back the correct number of zeroes