Question

A proton and an alpha particle (charge = 2e, mass = 6.64 x 10⁻²⁷ kg) are initially at rest, separated by 5.52 × 10⁻¹⁵. If they are both released simultaneously, explain why you can't find their velocities at infinity using only conservation of energy.

Answer 1

Conservation of energy alone cannot determine the velocities of the proton and alpha particle at infinity. Conservation of linear and angular momentum also need to be considered.

Step-by-step explanation:

When considering the motion of particles through a conservative force field, such as the Coulomb interaction between charges, we can use the conservation of mechanical energy to analyze their behavior. However, in this scenario, we cannot find the velocities of the proton and alpha particle at infinity using only conservation of energy.

This is because the conservation of energy only allows us to determine the sum of the kinetic and potential energies at any given point in space. It does not provide information about the individual velocities of the particles.

To find the velocities at infinity, we need to consider the conservation of linear and angular momentum as well. These additional conservation laws will help us determine the final velocities of the particles once they have moved a sufficient distance from each other.