Determine the ratio of the electron's speed

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In summary, the ratio of the electron's speed to the speed of light is approximately 1/137. It is determined experimentally through various methods and remains constant regardless of the electron's energy or environment. This ratio is closely related to other fundamental constants and has practical applications in fields such as quantum mechanics, particle physics, and electronics.
  • #1
lovelylm1980
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Determine the ratio of the electron's speed over that of the proton at the end of their respective trajectories? KE = 5.29keV

My question is do I use the kinetic energy to get velocity of electron then proton separately, and afterwards divide the results to obtain the ratio?
 
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  • #2
That's what I would do.
 
  • #3
electron: m, v
proton: M, u

mv²/2 = Mu²/2
mv² = Mu²
v²/u² = M/m
v/u = sqrt(M/m) = sqrt(1836) = 42.85

(valid for v << c)
 

1. What is the ratio of the electron's speed to the speed of light?

The ratio of the electron's speed to the speed of light is approximately 1/137. This means that the electron's speed is about 1/137th of the speed of light.

2. How is the ratio of the electron's speed determined?

The ratio of the electron's speed is determined experimentally through various methods, such as measuring the deflection of electrons in a magnetic field or studying the energy levels of electrons in an atom.

3. Is the ratio of the electron's speed constant?

Yes, the ratio of the electron's speed to the speed of light is a constant value and does not change. This means that regardless of the energy or environment of the electron, its speed will always be 1/137th of the speed of light.

4. How does the ratio of the electron's speed relate to other fundamental constants?

The ratio of the electron's speed is closely related to other fundamental constants, such as the fine structure constant and the Planck constant. These constants play a crucial role in understanding the behavior of subatomic particles and the fundamental laws of physics.

5. Does the ratio of the electron's speed have any practical applications?

Yes, the ratio of the electron's speed has several practical applications in fields such as quantum mechanics, particle physics, and electronics. It is also used in calculations and equations to describe the behavior of electrons and other subatomic particles.

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