How Does Electron Kinetic Energy Compare to Hydrogen's Ground State?

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In summary, the conversation discusses the kinetic energy of an electron with a de Broglie wavelength equal to the diameter of a hydrogen atom in its ground state. Using the equations λ = h/mv and diameter = 2 x Bohr radius, the kinetic energy is calculated to be 1.17e-20 J or 0.0732 eV. The issue of using the incorrect mass of the electron is also addressed.
  • #1
Woopy
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Homework Statement



An electron has a de Broglie wavelength equal to the diameter of a hydrogen atom in its ground state.
What is the kinetic energy of the electron?

How does this energy compare with the ground-state energy of the hydrogen atom?

Homework Equations



λ = h /mv
diameter = 2 x bohr radius = 1.06e-10 m

The Attempt at a Solution



1.06e-10 = 6.63e-34/1.67e-27v
v = 3.75e3 m/s
.5(1.67e-27)(3.75e3)^2 = 1.17e-20 J = .0732 eV
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.
 
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  • #2
Woopy said:

Homework Statement



An electron has a de Broglie wavelength equal to the diameter of a hydrogen atom in its ground state.
What is the kinetic energy of the electron?

How does this energy compare with the ground-state energy of the hydrogen atom?

Homework Equations



λ = h /mv
diameter = 2 x bohr radius = 1.06e-10 m

The Attempt at a Solution



1.06e-10 = 6.63e-34/1.67e-27v
v = 3.75e3 m/s
.5(1.67e-27)(3.75e3)^2 = 1.17e-20 J = .0732 eV
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.


Well, your electron mass doesn't look right at all. I suspect that you used the value for the proton mass rather than the electron mass. They're different by a factor of more than 1000.
 
  • #3
hah that was it. Thanks
 

FAQ: How Does Electron Kinetic Energy Compare to Hydrogen's Ground State?

1. What is Broglie Wavelength?

Broglie Wavelength is a concept in quantum mechanics that describes the wavelength of a particle. It is named after physicist Louis de Broglie, who proposed the idea that particles, such as electrons, have wave-like properties.

2. How is Broglie Wavelength calculated?

The Broglie Wavelength is calculated using the equation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle.

3. What is the significance of Broglie Wavelength?

The Broglie Wavelength is significant because it helps us understand the duality of particles, which can behave like both particles and waves. It also plays a crucial role in the study of quantum mechanics and the behavior of subatomic particles.

4. Can all particles have a Broglie Wavelength?

Yes, according to the theory of quantum mechanics, all particles have a corresponding Broglie Wavelength. However, the wavelength for macroscopic objects, such as a baseball, would be too small to be detectable.

5. How is Broglie Wavelength related to Heisenberg's Uncertainty Principle?

Broglie Wavelength is related to Heisenberg's Uncertainty Principle as it helps us understand the uncertainty in the position and momentum of a particle. The smaller the wavelength, the more accurately we can determine the position of the particle, but the less accurately we can determine its momentum.

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