The Large Hadron Collider, currently the world's most famous particle accelerator, generatesa beam of protons (mass m, = 1.7 × 10-27 kg), and a beam of anti-protons (which have thesame mass as protons), with the same speed, moving in the opposite direction. The machinecollides the protons with the antiprotons to see what they leave behind. Famously, in 2012,the experiment reached a high-enough energy scale that a long-sought subatomic particle,the "Higgs Boson" was formed, which they found to have a mass my = 2.2 × 10-25 kg. We'lldo this problem in MKS units, so recall that c= 3.00 x 10%m/s.Part A: Consider the collision of a single proton with a single antiproton, merging to forma single Higgs. Calculate the "gamma factor" y for the proton or the antiproton. (Note:because the protons and the antiprotons have equal masses and equal-but-opposite velocities,their y values will be the same, and the total momentum before the collision will be zero.)Part B: Calculate the work that the accelerator needs to do to accelerate a single proton tothis relativistic speed. (The number will not be large, but of course there are many particlesin the beams.)

Given: Mass of proton '' mp=1.7×10-27kg '' Mass of anti-proton mp¯=1.7×10-27kg Speed of proton…

The Large Hadron Collider, currently the world's most famous particle accelerator, generates a beam of protons (mass m, = 1.7 × 10–27 kg), and a beam of anti-protons (which have the same mass as protons), with the same speed, moving in the opposite direction. The machine collides the protons with the antiprotons to see what they leave behind. Famously, in 2012, the experiment reached a high-enough energy scale that a long-sought subatomic particle, the "Higgs Boson" was formed, which they found to have a mass my = 2.2 × 10-25 kg. We'll do this problem in MKS units, so recall that c= 3.00 × 10°m/s. Part A: Consider the collision of a single proton with a single antiproton, merging to form a single Higgs. Calculate the "gamma factor"y for the proton or the antiproton. (Note: because the protons and the antiprotons have equal masses and equal-but-opposite velocities, values will be the same, and the total momentum before the collision will be zero.) their Part B: Calculate the work that the accelerator needs to do to accelerate a single proton to this relativistic speed. (The number will not be large, but of course there are many particles in the beams.)

The Large Hadron Collider, currently the world's most famous particle accelerator, generates a beam of protons (mass m, = 1.7 × 10–27 kg), and a beam of anti-protons (which have the same mass as protons), with the same speed, moving in the opposite direction. The machine collides the protons with the antiprotons to see what they leave behind. Famously, in 2012, the experiment reached a high-enough energy scale that a long-sought subatomic particle, the "Higgs Boson" was formed, which they found to have a mass my = 2.2 × 10-25 kg. We'll do this problem in MKS units, so recall that c= 3.00 × 10°m/s. Part A: Consider the collision of a single proton with a single antiproton, merging to form a single Higgs. Calculate the "gamma factor"y for the proton or the antiproton. (Note: because the protons and the antiprotons have equal masses and equal-but-opposite velocities, values will be the same, and the total momentum before the collision will be zero.) their Part B: Calculate the work that the accelerator needs to do to accelerate a single proton to this relativistic speed. (The number will not be large, but of course there are many particles in the beams.)