Electron accelerated through a potential difference

In summary, the conversation discusses the attempt to find the velocity and momentum of an electron that has been accelerated through a potential difference of 1x10^6 V. The equations used are K=(1/2)mv^2 and v=sqrt(2K/m), but the resulting calculation of v=1.98c is incorrect due to the highly relativistic nature of the situation. The question then arises of how to find the correct value for kinetic energy and momentum.
  • #1
seanc12
15
0

Homework Statement


I am trying to get the velocity of an electron which has been accelerated through a potential difference of 1x106 V, so that i can find its momentum.

Homework Equations


K=(1/2)mv2
v=sqrt(2K/m)

The Attempt at a Solution


So , K = 1x106eV and m = 0.511x106eV/c2

v=sqrt(2x1x106/.511x106eV/c2)

then the c2 comes out and I am left with

v=sqrt(2x1x106[/SUPeV]/.511x106eV)c

v=1.98c

which is clearly wrong since v can't be higher than the speed of light,
what am i overlooking?
 
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  • #2
An electron passing through a 1x10^6 V potential is a highly relativistic situation. The kinetic energy you wrote down is no longer true.
 
  • #3
So, how do i find K, or the momentum for that matter?
 

FAQ: Electron accelerated through a potential difference

1. What is an electron accelerated through a potential difference?

An electron accelerated through a potential difference is a process in which an electron is given energy and accelerated by passing it through a potential difference, or a voltage. This increases the speed and kinetic energy of the electron, allowing it to move through a circuit or other medium.

2. How does an electron accelerate through a potential difference?

An electron accelerates through a potential difference due to the electric field created by the potential difference. This electric field exerts a force on the electron, causing it to accelerate in the direction of the field. The electron gains kinetic energy as it moves through the field.

3. What is the relationship between potential difference and electron acceleration?

The relationship between potential difference and electron acceleration can be described by the equation: F = qE, where F is the force exerted on the electron, q is the charge of the electron, and E is the electric field strength. This shows that as the potential difference increases, the electric field strength also increases, resulting in a greater force and acceleration on the electron.

4. How is the acceleration of an electron through a potential difference measured?

The acceleration of an electron through a potential difference can be measured using an oscilloscope or voltmeter. These devices measure the potential difference between two points and can calculate the electric field strength and force exerted on the electron. The acceleration of the electron can then be determined using the equation a = F/m, where a is the acceleration, F is the force, and m is the mass of the electron.

5. What are some real-world applications of an electron accelerated through a potential difference?

An electron accelerated through a potential difference has many practical applications. It is used in devices such as cathode ray tubes, where the accelerated electrons produce images on a screen. It is also used in particle accelerators, which are used in scientific research and medical treatments. Additionally, electron microscopes use this principle to produce highly detailed images of microscopic objects. In electronics, the acceleration of electrons through potential differences is crucial for the functioning of many devices, such as transistors and computer chips.

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