De Broglie Wavelengths: Need clarification for questions.

In summary: I think I can solve this problem, the wavelength cannot be greater the spacing between the walls, but the formula given uses "Å" as the units, and I'm not sure what the "Å" means. The allowed kinetic energy of a neutron in between two walls at a distance of 1000 Å is:E = h*m*v^2where h is the Planck constant and m is the mass of the neutron.
  • #1
12
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Thanks for any help you can give. I just started modern physics and my teacher has a tendency to give questions that were based on things not mentioned in the book and only briefly mentioned in the lectures, so I'm a bit confused.

Homework Statement



1) Calculate the distribution function of the de Broglie wavelengths of atoms in the thermal equilibrium gas. The gas temp. is T and the atomic mass is M. What is the most probable de Broglie wavelength?

2)A neutron moves between two parallel impenetrable walls and the neutron velocity stays perpendicular to the wall surfaces. Distance between the walls is L = 1000 Å. Determine all allowed kinetic energies of a neutron, if its motion is described by standing de Broglie waves.

Homework Equations


The Attempt at a Solution



1) While I would love to attempt the solution. What is "the thermal equilibrium gas"? I've never heard the term before and I couldn't find anything on google about it.

2) I think I know how to solve the problem, the wavelength cannot be greater the spacing between the walls, but the formula given uses "Å" as the units, and I'm not sure what the "Å" means.

I had the same Physics prof for two straight years, and he always gave problems directly from the book, so I'm not used to not being able to directly reference back to stuff.
 
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  • #2
That A thing is the symbol for an angstrom, 10^-10 I think

For the first one I think they're saying the gas is at thermal equilibrium, so you can say the average kinetic energy = 3/2*K*T
 
  • #3
Thank you so much--especially with the first one. Now I can actually do the problems.
 
  • #4
Malitic said:
1) What is "the thermal equilibrium gas"? I've never heard the term before and I couldn't find anything on google about it.
Distribution of molecular velocities in termal equilibrium gas is Maxwell-Boltzmann distribution.
 

1. What are De Broglie wavelengths?

De Broglie wavelengths are a concept in quantum mechanics that describe the wavelength associated with a moving particle, such as an electron. They are named after French physicist Louis de Broglie, who proposed the idea that particles can exhibit wave-like behavior.

2. How are De Broglie wavelengths calculated?

The De Broglie wavelength of a particle can be 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. This equation is derived from the de Broglie relation, which states that the momentum of a particle is equal to Planck's constant divided by its wavelength.

3. What is the significance of De Broglie wavelengths?

The concept of De Broglie wavelengths helps to explain the wave-particle duality of matter, which is a fundamental principle of quantum mechanics. It also plays a crucial role in understanding the behavior of particles at the quantum level, such as in the double-slit experiment.

4. How are De Broglie wavelengths related to the uncertainty principle?

The uncertainty principle, proposed by German physicist Werner Heisenberg, states that it is impossible to know both the position and momentum of a particle with absolute certainty. De Broglie wavelengths are related to this principle because they represent a fundamental limit on the precision with which we can measure the position and momentum of a particle.

5. Can De Broglie wavelengths be observed in real-life situations?

Yes, De Broglie wavelengths have been observed in a variety of experiments, such as the diffraction of electrons through a crystal lattice and the interference patterns of particles in the double-slit experiment. These phenomena provide strong evidence for the wave-like behavior of particles at the quantum level.

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