De Broglie wavelength of an electron and speed

In summary, the de Broglie wavelength of an electron is 6.4e-10m. Its speed is 1.136e6 m/s and the voltage needed to accelerate it to this speed is 3.7 V.
  • #1
xelda
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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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  • #2
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?
 
  • #3
Awesome. Thank you so much for your help!
 

FAQ: De Broglie wavelength of an electron and speed

What is the De Broglie wavelength of an electron?

The De Broglie wavelength of an electron is a quantum mechanical concept that describes the wave-like behavior of matter. It is the wavelength of a matter wave associated with an electron and is given by the equation λ = h/mv, where h is Planck's constant, m is the mass of the electron, and v is its velocity.

How is the De Broglie wavelength related to the speed of an electron?

The De Broglie wavelength is inversely proportional to the speed of an electron. This means that as the speed of the electron increases, its wavelength decreases. This relationship is described by the equation λ = h/mv, where v is the velocity of the electron.

What is the significance of the De Broglie wavelength of an electron?

The De Broglie wavelength of an electron is significant because it demonstrates the wave-particle duality of matter. It shows that matter, like light, can exhibit both wave-like and particle-like properties. This concept is fundamental to understanding the behavior of particles at the quantum level.

Can the De Broglie wavelength of an electron be measured?

Yes, the De Broglie wavelength of an electron can be measured using various experimental techniques such as electron diffraction or electron microscopy. These methods involve passing electrons through a diffraction grating or a thin sample and measuring the resulting interference pattern to determine the wavelength of the electrons.

How does the De Broglie wavelength of an electron differ from the De Broglie wavelength of other particles?

The De Broglie wavelength of an electron is unique to electrons and other subatomic particles. The equation λ = h/mv can also be applied to other particles, but the value of Planck's constant (h) and the mass (m) will be different, resulting in different wavelengths. Additionally, the De Broglie wavelength for larger objects, such as macroscopic objects, is so small that it is practically negligible.

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