Finding speed of two electrons initially at rest

In summary, the problem involves two electrons starting at rest with a separation of 5.0 x 10^-12 m and accelerating away from each other. To calculate the speed of each electron when they are a very large distance apart, the equations for electric potential energy and kinetic energy are used. However, the original attempt at a solution did not take into account that both electrons would end up with kinetic energy. Taking this into consideration, the correct speed for each electron is 7.1 x 106 m/s.
  • #1
ozbii
4
0

Homework Statement


Two electrons start at rest with a separation of 5.0 x 10^-12 m. Once released, the electrons accelerate away from each other. Calculate the speed of each electron when they are a very large distance apart (Ee = 0).

Homework Equations


EE = kQq/r
Ek = (1/2)mv2

The Attempt at a Solution


EE2 - EE1 = - (Ek2 - Ek1)
- EE1 = - Ek2
(kq2) / r = (1/2)mv2
v = sqrt[ 2(8.99 x 109)(-1.6 x 10-19)2 / (9.11 x 10-31)(5.0 x 10-12) ]
v ≅ 1.0 x 107 m/s

The answer is apparently 7.1 x 106 m/s
[/B]
 
Physics news on Phys.org
  • #2
Hello, and welcome to PF!

Do both electrons end up with some kinetic energy? Did you take that into account?
 
  • #3
TSny said:
Hello, and welcome to PF!Do both electrons end up with some kinetic energy? Did you take that into account?
Thanks for replying!
Oh I don't think I did. So it would be Ee1 = (1/2)mv^2 + (1/2)mv^2.
 
  • #4
Yes. Are you assuming that the two electrons end up with the same speed? Can you justify that?
 
  • Like
Likes dndmmhd

1. How do you find the speed of two electrons initially at rest?

In order to find the speed of two electrons initially at rest, you will need to use the equation KE = 1/2mv2, where KE is the kinetic energy, m is the mass of the electron, and v is the velocity. You will also need to use the conservation of momentum equation p1 + p2 = 0, where p1 and p2 are the initial momenta of the two electrons. By solving these equations simultaneously, you can find the velocity of the electrons.

2. Why are the electrons initially at rest?

Electrons are typically considered to be at rest when they are not in motion or when their velocity is zero. In this scenario, it is assumed that the electrons are initially at rest to simplify the calculations and focus on the change in their velocity due to the applied force.

3. How does the mass of the electrons affect their speed?

The mass of an electron does not affect its speed, but it does affect its kinetic energy. According to the equation KE = 1/2mv2, the kinetic energy is directly proportional to the mass of the electron. This means that a higher mass electron would have a higher kinetic energy and therefore a higher speed compared to a lower mass electron under the same conditions.

4. What is the significance of finding the speed of two electrons initially at rest?

Finding the speed of two electrons initially at rest can help us understand the behavior of particles in a system and how they interact with each other. It can also be used to calculate other important quantities such as momentum and energy, which can have practical applications in various scientific fields.

5. Can this concept be applied to other particles besides electrons?

Yes, this concept can be applied to any particles as long as they are initially at rest and the necessary equations for kinetic energy and conservation of momentum are used. It is a fundamental principle in physics that applies to all particles and can help us understand their behavior and interactions in different scenarios.

Similar threads

Find the drift speed of electrons in a wire
    • Introductory Physics Homework Help
Replies
2
Views
1K
Electron between two parallel plates
    • Introductory Physics Homework Help
Replies
6
Views
2K
Initial speed of the proton?
    • Introductory Physics Homework Help
Replies
2
Views
2K
Potential difference to achieve speed
    • Introductory Physics Homework Help
Replies
4
Views
982
Determining angular frequency in an electric field using velocity.
    • Introductory Physics Homework Help
Replies
15
Views
2K
What Is the Escape Speed of an Electron from a Charged Glass Sphere?
    • Introductory Physics Homework Help
Replies
2
Views
8K
Find the voltage needed to accelerate the electron from rest
    • Introductory Physics Homework Help
Replies
7
Views
10K
Finding the displacement of an electron between 2 charged rods
    • Introductory Physics Homework Help
Replies
11
Views
1K
Calculating Electron Speed Between Parallel Charged Plates
    • Introductory Physics Homework Help
Replies
3
Views
1K
Finding the Kinetic Energy using the mass, radius and initial KE
    • Introductory Physics Homework Help
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top