De Broglie wavelength of an electron and speed

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SUMMARY

The de Broglie wavelength of an electron is given as λ = 6.4e-10 m, leading to a calculated speed of 1.136e6 m/s using the formula v = h/mλ. The kinetic energy (KE) was determined to be 5.883e-19 J, which converts to 3.677 eV. However, the voltage required to accelerate the electron to this speed is 3.7 V, not 3.7 eV, highlighting a common unit conversion error in the discussion.

PREREQUISITES
  • Understanding of de Broglie wavelength and its application to particles
  • Familiarity with the equation v = h/mλ for calculating speed
  • Knowledge of kinetic energy calculations using KE = 1/2mv^2
  • Basic principles of voltage and energy conversion between joules and electronvolts
NEXT STEPS
  • Study the relationship between kinetic energy and voltage in particle physics
  • Learn about the implications of de Broglie wavelength in quantum mechanics
  • Explore advanced applications of the de Broglie equation in electron microscopy
  • Investigate common pitfalls in unit conversions in physics problems
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Students in physics, particularly those studying quantum mechanics and particle physics, as well as educators looking to clarify concepts related to de Broglie wavelength and energy calculations.

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Homework Statement


An electron has a de Broglie wavelength of λ = 6.4e-10m.
What is its speed? What voltage was needed to accelerate to this speed?


Homework Equations


v=h/mλ

KE = 1/2mv^2


The Attempt at a Solution


I already determined that the speed is 1.136e6 m/s. Finding the voltage is what has me stumped. Using KE = 1/2mv^2, I found KE is 5.883e-19 J. I converted this to eV, so KE = 3.677 eV.

With sig figs taken into account, the answer (I think) is supposed to be 3.7 eV but the online homework isn't accepting it. I feel like it shouldn't be hard, but I can't see what I did wrong. Any help would be appreciated!
 
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I get pretty much the same thing you did. But did you really put 3.7 eV in? Because that's the kinetic energy. The question is asking for the voltage to accelerate it. That's just 3.7 V not eV. Did you put the wrong units in?
 
Awesome. Thank you so much for your help!
 

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