A positron (a particle with a charge of +e and a mass equal...

A positron (a particle with a charge of $+e$ and a mass equal to that of an electron) that is accelerated from rest between two points at a fixed potential difference acquires a speed of $9.0 \times 10^{7} \mathrm{m} / \mathrm{s}$. What speed is achieved by a proton accelerated from rest between the same two points? (Disregard relativistic effects.

Key Concepts

Electric Potential Difference

This refers to the difference in electric potential between two points, which determines the amount of work done per unit charge in moving a charge between those points. In particle acceleration, it defines how much energy is imparted to a charged particle as it moves through an electric field.

Kinetic Energy in a Non-Relativistic Context

For non-relativistic speeds, the kinetic energy of a particle is given by the formula (1/2)m*v². When a particle is accelerated from rest by an electric potential difference, the work done on the particle is converted into its kinetic energy. This relationship allows us to determine the final speed of the particle using energy conservation.

Mass-to-Charge Ratio

The mass-to-charge ratio is crucial in determining the acceleration of a particle under the influence of an electric field. For two particles that undergo acceleration through the same potential difference, the particle with a lower mass or a higher charge-to-mass ratio will generally achieve a greater final speed, due to receiving more acceleration from the same energy input.

Energy Conservation

Energy conservation is the principle that the total energy in an isolated system remains constant. In the context of particles accelerated by a potential difference, the total electric potential energy lost is converted into kinetic energy. This principle provides the basis for calculating the speed achieved by the particle after acceleration.

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