Find the voltage needed to accelerate the electron from rest

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SUMMARY

The discussion focuses on calculating the voltage required to accelerate an electron from rest to a speed of 1.1384 x 1011 m/s, derived from its wavelength of 6.4 x 10-15 m. The mass of the electron is 9.1 x 10-31 kg, and its charge is 1.6 x 10-19 C. The relationship between voltage and kinetic energy is established through the equation E = eV = mv2/2, emphasizing the conservation of energy principle. The discussion also touches on the necessity of considering relativistic effects for speeds approaching the speed of light.

PREREQUISITES
  • Understanding of wave-particle duality and de Broglie wavelength
  • Familiarity with the concepts of kinetic energy and potential energy
  • Knowledge of the conservation of energy principle
  • Basic understanding of special relativity and its implications on particle speed
NEXT STEPS
  • Learn how to apply the de Broglie wavelength formula in various contexts
  • Study the relationship between voltage and kinetic energy in charged particles
  • Explore the implications of special relativity on particle speeds and energy calculations
  • Investigate the concept of relativistic momentum and its calculations
USEFUL FOR

Students in physics, particularly those studying electromagnetism and quantum mechanics, as well as educators seeking to clarify concepts related to electron acceleration and energy transformations.

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Homework Statement


An electron moving with a speed v can behave as wave with wavelength 6.4 x 10^-15 m. Given that the mass of electron = 9.1 x 10^-31 kg and the charge of electron is 1.6 x 10^-19 C, find
(a) the speed of v of the electron, and
(b) the voltage needed to accelerate the electron from rest until it acquires the speed v.

Homework Equations

The Attempt at a Solution



(a) wavelength = h / mv
v = h/ (m x wavelength)
= 1.1384 X 10^11 m/s

How do I calculate (b)? Please help, thank you. Kindly correct me if (a) is wrong.
 
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You are dealing with non-relativistic electron, right ? In that case i don't see any mistake in (a)
(b) Energy = charge * voltage, can you translate that to kinetic energy and pull a speed out of there ?
[EDIT: In case i wasn't clear, the potential energy which is E = e*V translates to kinetic energyenergy but that fact, e*V = mv^2 /2]
 
Last edited:
The electron gains kinetic energy when moving at the speed you found. Think of the conservation of energy and from where it gained that energy.
 
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0coffeebean0 said:

Homework Statement


An electron moving with a speed v can behave as wave with wavelength 6.4 x 10^-15 m. Given that the mass of electron = 9.1 x 10^-31 kg and the charge of electron is 1.6 x 10^-19 C, find
(a) the speed of v of the electron, and
(b) the voltage needed to accelerate the electron from rest until it acquires the speed v.

Homework Equations

The Attempt at a Solution



(a) wavelength = h / mv
v = h/ (m x wavelength)
= 1.1384 X 10^11 m/s

How do I calculate (b)? Please help, thank you. Kindly correct me if (a) is wrong.
What is the speed of light? Can you use the rest mass of electron to calculate the momentum? See:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html
 
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Noctisdark said:
You are dealing with non-relativistic electron, right ?
Can anything travel with 1.1384 X 10^11 m/s speed?
 
ehild said:
Can anything travel with 1.1384 X 10^11 m/s speed?
Classically, Yes .
 
What is the speed of light?
Noctisdark said:
Classically, Yes .
And in reality?
 
ehild said:
What is the speed of light?

And in reality?
It doesn't, but people before the 19th thought that it was possible either way, you are extremely right, but as a homework he should use special relativity, i think, however sorry for that .
 

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