(a) Calculate the speed of a proton that is accelerated from...

Name: Problem 1, Chapter 25: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2020-05-30T18:18:15-08:00
Duration: 2 min 42 s
Channel: Mayukh Banik
Description: (a) Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 120 V. (b) Calculate the speed of an electron that is accelerated through the same electric potential difference.

(a) Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 120 V. (b) Calculate the speed of an electron that is accelerated through the same electric potential difference.

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Key Concepts

Electric Potential Difference

This is the measure of the work done per unit charge as a charge moves between two points in an electric field. It is the driving force that accelerates charged particles, and the energy gained by a particle is the product of its charge and the voltage difference.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. In particle acceleration problems, the electrical potential energy that a charged particle gains when passing through a voltage is entirely converted into kinetic energy (ignoring losses), which allows us to compute its speed.

Kinetic Energy and Velocity Relationship

The kinetic energy of a particle moving at speed v is given by the formula (1/2)mv². By equating the kinetic energy with the electrical energy (qV), one can derive an expression for the speed of the particle, typically v = sqrt(2qV/m).

Particle Properties (Mass and Charge)

Different particles, such as protons and electrons, have distinct masses and charges. These intrinsic properties mean that even when subjected to the same potential difference, the resulting speeds will differ since the acceleration depends on the ratio of the particle's charge to its mass.

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