# Accelerating electrons

• Gyroscope
In summary, an electron is accelerated from rest through a potential difference of V volts, and the question is asking for the final velocity. The attempted solution used relativistic energy but resulted in an unreal answer. The correct approach is to use the relativistic kinetic energy, taking into account the fact that the electron is accelerated from rest.

## Homework Statement

An electron is accelerated from rest through a potential difference of V volts. What is the final velocity?

I did:
$$qV=\frac{mc^2}{\sqrt{1-\frac{v_f^2}{c^2}}}$$

And solve for v, but I get an unreal answer. What am I doing wrong?!

## The Attempt at a Solution

Why are you using relativistic energy?

Because there is an high potential difference. If I use non-relativistic energy it gives a speed higher than the speed of light.

Could you post more of the question and your work?

If I'm not mistaken(Memory sometimes betray me) qV=(Gamma-1)mc^2

ziiad this is the relativistic kinetic energy, what I need is the relativistic change in kinetic energy.

No, you are right. What a stupid mistake of mine. :( Thanks, mate.

Don't worry, we all make mistakes, they key part was "...accelerated from rest..."

## 1. What is meant by "accelerating electrons"?

Accelerating electrons refers to the process of increasing the speed or velocity of electrons through the application of electric fields or electromagnetic waves.

## 2. How do scientists accelerate electrons?

Scientists can accelerate electrons using various methods such as using particle accelerators, applying high voltage electric fields, or using lasers to generate electromagnetic waves.

## 3. What is the significance of accelerating electrons in scientific research?

Accelerating electrons allows scientists to study the behavior and properties of particles at high energies, which can provide insights into the fundamental nature of matter and the universe. It also has practical applications in fields such as medical imaging and particle therapy.

## 4. Can accelerating electrons cause any harm?

Yes, accelerating electrons can be potentially harmful if not properly controlled. For example, in medical imaging, excessive exposure to accelerated electrons can cause tissue damage. Therefore, strict safety measures are in place when working with accelerated electrons.

## 5. What are some challenges scientists face when working with accelerated electrons?

One of the main challenges is maintaining the stability and precision of the electron beam as it travels at high speeds. Another challenge is minimizing the loss of energy due to interactions with the surrounding environment, such as air molecules, which can affect the accuracy of experiments.

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