De Broglie Wavelength of an electron

In summary, the velocity of the electron in the ground state of the hydrogen atom is 2.6 x 10^8 m/s, which is much less than the speed of light. Using De Broglie's equation, the wavelength of this electron is calculated to be approximately 1.7 x 10^-12 meters. This is consistent with De Broglie's hypothesis about the allowed energies of the electron. However, since the electron is not moving at relativistic speeds, the difference between this calculated wavelength and the actual wavelength may not be significant.
  • #1
Janet
1
0
1. The velocity of the electron in the ground state of the hydrogen atom is 2.6 x 10^8 m/s. What is the wavelength of this electron in meters?2. De Broglie's equation: lamda = h/p
p=mv

The Attempt at a Solution

...

(6.626 x 10^-34) / (2.6 x 10^8 x 9.11 x 10^-31)

= 2.798 x 10^-12 meters

This isn't the right answer...obviously...[/B]
 
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  • #2
Quickly (sorry, posting and running), and with wolfram alpha, I get 1.7 * 10^-12 m. Which doesn't sound too far off to me (and neither does your answer), considering 2.6 * 10^8 m/s is about 500 keV of kinetic energy for an electron.

Why do you suspect your answer wrong?
 
  • #3
Is the electron relativistic enough to make a difference?
Is the wavelength consistent with DeBroglie's hypothesis about the allowed energies of the electron?
 
  • #4
Janet said:
1. The velocity of the electron in the ground state of the hydrogen atom is 2.6 x 10^8 m/s. What is the wavelength of this electron in meters?
Check the problem text. The speed of the electron is much less than the speed of light in the ground state of the H atom.

ehild
 
  • #5


There seems to be a mistake in the calculation. The correct equation to use for the de Broglie wavelength of an electron is λ = h/mv, where h is Planck's constant, m is the mass of the electron, and v is its velocity. Therefore, the correct calculation would be:

λ = (6.626 x 10^-34 m^2 kg/s) / (9.11 x 10^-31 kg) * (2.6 x 10^8 m/s)

= 2.42 x 10^-10 meters

This result is in agreement with the expected de Broglie wavelength for an electron in the ground state of a hydrogen atom. It is important to note that the de Broglie wavelength is a fundamental property of particles, and it can provide insight into their wave-like nature. In this case, the short wavelength of the electron suggests that it has a high probability of being found near the nucleus of the hydrogen atom.
 

1. What is the De Broglie Wavelength of an electron?

The De Broglie Wavelength of an electron is a concept in quantum mechanics that describes the wavelength of a particle, such as an electron, in motion. It is named after French physicist Louis de Broglie, who proposed that all particles exhibit wave-like behavior.

2. How is the De Broglie Wavelength of an electron calculated?

The De Broglie Wavelength of an electron is calculated using the following equation: λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the electron, and v is its velocity. This equation relates the particle's momentum and wavelength.

3. 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 particles in quantum mechanics. It also helps to explain phenomena such as diffraction and interference, which are typically associated with waves.

4. How does the De Broglie Wavelength of an electron relate to the uncertainty principle?

The De Broglie Wavelength of an electron is related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The smaller the wavelength, the more accurately we can know the momentum of an electron, but the less accurately we can know its position.

5. Can the De Broglie Wavelength of an electron be observed experimentally?

Yes, the De Broglie Wavelength of an electron has been observed experimentally in various experiments, such as the Davisson-Germer experiment and the electron diffraction experiment. These experiments provide evidence for the wave-like nature of particles.

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