Question

Consider a perfectly elastic collision between two particles. Initially the 1st particle with a mass, m, is moving in the x-direction with a velocity, v1 , and the 2nd particle with mass, M is at rest. After the collision, the 1st particle has a purely y-directional velocity. Determine the velocity components for both particles following the collision and the kinetic energy of the 2nd particle (The one initially at rest). Consider the cases of: a) an electron striking a hydrogen atom, b) an electron striking a xenon atom, and c) a xenon atom striking another xenon atom. For each case assume the incident particle velocity is 5000 m/s.

Answer 1

To solve for the velocities of particles after a perfectly elastic collision, one must apply the conservation of momentum in both the x and y directions and the conservation of kinetic energy. Without the actual masses of the particles involved, like an electron, a hydrogen atom, or a xenon atom, one can only provide a generic solution framework. With the respective masses, the final velocities and kinetic energies can be calculated explicitly.

Step-by-step explanation:

When considering a perfectly elastic collision between two particles, we use both the conservation of momentum and conservation of kinetic energy to determine the velocities of the particles after collision. Since the collision is perfectly elastic, we know that kinetic energy is conserved. Let us define m as the mass of the first particle moving with velocity v1, and M as the mass of the second particle initially at rest.

For a collision in two dimensions, we apply the conservation of momentum in both the x and y directions separately. The conservation of momentum in the x-direction and y-direction (since the first particle ends with a purely y-directional velocity) will give us two equations. We also have the conservation of kinetic energy giving us a third equation. These can be used to solve for the final velocities.

However, to provide specific numbers for each scenario, it is necessary to know the exact masses of the particles engaging in the collision. Since the question does not provide this information, we can only give a generic framework without numeric solutions. The student is expected to insert the respective masses of an electron, a hydrogen atom, and a xenon atom. After inserting the masses and the initial velocity of 5000 m/s for the incident particle, solving the equations simultaneously will yield the velocity components for both particles and the kinetic energy of the previously stationary particle for each case.