Calculate the speed of a proton that is accelerated from rest through an electric potential diff

step 1 So basically the electron and the proton is not accelerated by the same potential elephants so w

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

Key Concepts

Mass Difference Among Particles

Protons and electrons have very different masses, so even when subjected to the same potential difference, they will acquire different speeds. Recognizing that mass affects acceleration is crucial in predicting and comparing the behavior of different charged particles under identical conditions.

Kinetic Energy of Particles

This concept involves the formula ½ mv², where m is the mass of the particle and v is its velocity. It directly connects the energy imparted to the particle with its resulting speed, which is critical when assessing how different particles respond to the same energy input.

Non-relativistic Approximation

In scenarios where the kinetic energy imparted is much smaller than the rest energy of the particle (i.e., speeds are significantly less than the speed of light), the non-relativistic equations for kinetic energy are sufficient. This assumption simplifies calculations and is typically valid for relatively low voltage accelerations such as 120 V.

Electric Potential Energy

This concept relates to the energy stored by a charged particle in an electric field. When a particle with charge q moves through a potential difference V, it gains or loses energy equal to qV. This relationship is essential in determining the energy available to be converted into kinetic energy when the particle is accelerated.

Conservation of Energy

The work-energy principle states that the work done on a particle by the electric field is converted into the particle’s kinetic energy. This is expressed mathematically by equating the electrical work (qV) to the kinetic energy (½ mv²), allowing for the calculation of a particle's speed after acceleration.

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