Calculating Properties of a 2.2 eV Electron

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Homework Help Overview

The discussion revolves around calculating various properties of a 2.2 eV electron, including energy, rest mass, speed, wavelength, and momentum. Participants are exploring the implications of kinetic energy in both classical and relativistic contexts.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants express confusion regarding the meaning of 2.2 eV and its relation to kinetic energy. There is discussion about using the rest mass and whether to apply classical mechanics or relativistic equations for speed calculations. Questions arise about the implications of speed relative to the speed of light and the need for different approaches if relativistic effects are significant.

Discussion Status

The conversation is active, with participants sharing calculations and questioning the appropriateness of different methods. Some guidance is provided regarding the use of Newtonian physics versus relativistic formulas, but no consensus on a single approach has been reached.

Contextual Notes

Participants are navigating the complexities of quantum mechanics and special relativity, indicating a potential gap in understanding the underlying principles of the topic. There is an emphasis on the need for clarity regarding the conditions under which different physics equations apply.

EgpYo
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Homework Statement



I need to figure out the energy, rest mass, speed, wavelength and momentum of a 2.2 eV electron. Thats all it says.

Homework Equations


Ek = 1/2mv^2

The Attempt at a Solution


I don't understand what 2.2 eV is. The kinetic energy?
This converts to 3.52x10^-19 J

Rest mass should be 9.11x10^-31. Or do I use E=mc^2? Why or why not?

No idea how to find speed, which I need to calculate wavelength and momentum. I could use Ek= 1/2mv^2 because the electron will not be traveling close to the speed of light, but I feel like this is not the way you SHOULD calculate it. There has to be another way.
 
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EgpYo said:

Homework Statement



I need to figure out the energy, rest mass, speed, wavelength and momentum of a 2.2 eV electron. Thats all it says.

Homework Equations


Ek = 1/2mv^2

The Attempt at a Solution


I don't understand what 2.2 eV is. The kinetic energy?
This converts to 3.52x10^-19 J
Yes, that'll be the kinetic energy.
Rest mass should be 9.11x10^-31. Or do I use E=mc^2? Why or why not?

No idea how to find speed, which I need to calculate wavelength and momentum. I could use Ek= 1/2mv^2 because the electron will not be traveling close to the speed of light, but I feel like this is not the way you SHOULD calculate it. There has to be another way.

Check the speed that you get when you apply Newtonian physics to find the speed from the KE . If its much less than the speed of light then you can continue with Newtonian physics and ignore relativistic effects. So, what value do you get for speed via 1/2mv2?
 
8.79x10^5 m/s
 
EgpYo said:
8.79x10^5 m/s
How does that compare to the speed of light (percentage-wise)?
 
Its 0.293% of the speed of light. But I'm mainly concerned about how to do the question without Ek=1/2mv^2. What if it WAS close to the speed of light? Is there a different procedure I can use?
 
EgpYo said:
Its 0.293% of the speed of light. But I'm mainly concerned about how to do the question without Ek=1/2mv^2. What if it WAS close to the speed of light? Is there a different procedure I can use?
Yes, you would need to invoke the formulas of special relativity to deal with how some of the energy ends up as an apparent increase in mass. Note though that the rest mass is always the same regardless. Rest mass is the mass of an object that is at rest with respect to the observer, so no corrections for speed are involved at all.
 
Can you outline the procedure? I really don't understand this last unit of quantum mechanics. Like what is the full equation? I would be solving for v
 
EgpYo said:
Can you outline the procedure? I really don't understand this last unit of quantum mechanics. Like what is the full equation? I would be solving for v
Well, the relativistic kinetic energy is given by:

$$KE = m_o c^2 \left[ \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1 \right] $$

and you would be looking for v, which will get a tad messy algebraically.
 

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