A particle accelerator collides beams of protons and anti-protons with equal and opposite momenta. The aim of this experiment is to create a possible new massive particle with neutral charge and rest mass 80 times that of a single proton. Calculate the necessary speed of the protons and anti-protons) in the collision as a % of the speed of light.
A) 85.92 %
B) 99.97 %
C) 98.72 %
D) 94.28 %
E) None of these is correct.

Question

Quizplus · Accepted Answer

The rest mass of the new particle is 80 times that of a proton. Therefore, its energy when at rest will be 80 times the energy of a proton at rest. This energy can be expressed using Einstein's famous equation, E=mc^2, as (80m_p)(c^2), where m_p is the rest mass of a single proton and c is the speed of light.

In order to create this particle, the total energy of the colliding protons and anti-protons must be at least equal to this energy. The total energy of a single proton or anti-proton can be expressed as E=γm_pc^2, where γ is the relativistic factor, given by γ=1/√(1-v^2/c^2), where v is the velocity of the particle.

Since the colliding protons and anti-protons have equal and opposite momenta, their total momentum is zero. Therefore, the total energy of the collision will be the sum of the energies of the individual protons and anti-protons, which can be calculated using the above equation.

Setting this energy equal to (80m_p)(c^2), and solving for v/c, we get:

v/c = √(1 - (1/81))

v/c ≈ 0.99973

So the speed of the protons and anti-protons must be approximately 99.97% of the speed of light. Therefore, the correct answer is B.

A Particle Accelerator Collides Beams of Protons and Anti-Protons with Equal