De Broglie wavelength and atom penetration

K/c as an approximation to the exact formula p = sqrt(E^2/c^2-m^2c^2), where E is the total energy of the particle (rest mass plus kinetic energy). In this problem, K is much larger than the rest mass, so the two formulas give essentially the same result.In summary, to calculate the de Broglie wavelength of an electron with kinetic energy 60 GeV, we can use the formula DBW = h/p, where p = K/c as an approximation for extremely relativistic situations. To find the percentage of an atom's diameter that the DBW can penetrate, we can compare it to the diameter of the Bohr model for the hydrogen atom in its
  • #1
Bakery87
11
0

Homework Statement



Calculate the de broglie wavelength (DBW) of an electron with kinetic energy 60 GeV.

What percentage of an atom's diameter can it penetrate?


Homework Equations



DBW = h/p
p=mv


The Attempt at a Solution



Basically I have an electron traveling at the speed of light. I arrived at this from its kinetic energy (60 GeV) and by using the relativistic K-energy equation. So I get it's de broglie wavelength fairly easily (I have this part done).

The part I don't understand is the penetration. I guess I just need some guidance/equations. Any ideas?
 
Physics news on Phys.org
  • #2
Welcome to PF, Barkery87.

For an atom's diameter, they might mean take the diameter of the Bohr model for the hydrogen atom in its ground state. What percentage of that diameter is the deBroglie wavelength?

p.s.
Um, you didn't use the electron's rest mass to calculate p=mv, did you?
 
  • #3
I used 0.511003 MeV/c^2
 
  • #4
Momentum is calculated differently for relativistic motion. There should be a formula in your textbook or lecture notes, relating E, p, and m (the rest mass, sometimes called m0)
 
  • #5
I did find something...

p = K/c

I'm still looking through my notes.
 
  • #6
Bakery87 said:
p = K/c

Actually, that's a valid approximation for extremely relativistic situations (like this one).
 

Related to De Broglie wavelength and atom penetration

1. What is the De Broglie wavelength and how is it related to atoms?

The De Broglie wavelength is a concept in quantum mechanics that describes the wave-like behavior of particles, including atoms. It is named after the French physicist Louis de Broglie, who proposed that particles, such as atoms, have both particle and wave properties. The De Broglie wavelength is related to the momentum of a particle, and can be calculated using the equation: λ = h/mv, where λ is the De Broglie wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.

2. How does the De Broglie wavelength affect the penetration of atoms?

The De Broglie wavelength is inversely proportional to the momentum of a particle. This means that as the momentum of an atom increases, its De Broglie wavelength decreases. As a result, atoms with higher momentum have shorter De Broglie wavelengths, which allows them to penetrate through smaller spaces and barriers, such as atomic nuclei and electron clouds.

3. Can the De Broglie wavelength be used to explain the behavior of electrons in an atom?

Yes, the De Broglie wavelength is an important concept in understanding the behavior of electrons in an atom. According to the Heisenberg uncertainty principle, it is impossible to know the exact position and momentum of an electron at the same time. Therefore, the De Broglie wavelength can be used to describe the probability of finding an electron in a certain region around the nucleus of an atom.

4. How does the De Broglie wavelength of an atom affect its energy level?

The De Broglie wavelength of an atom is directly related to its kinetic energy. As the De Broglie wavelength decreases, the kinetic energy of the atom increases. This is because shorter wavelengths correspond to higher momentum, which in turn leads to higher kinetic energy. Additionally, the De Broglie wavelength also affects the probability of finding an electron in a certain energy level, as the wavelength determines the size and shape of the electron's orbital.

5. Can the De Broglie wavelength be measured experimentally?

Yes, the De Broglie wavelength can be measured experimentally using techniques such as electron diffraction or neutron diffraction. These methods involve sending a beam of electrons or neutrons through a crystalline material and measuring the resulting diffraction pattern. By analyzing the diffraction pattern, the De Broglie wavelength of the particles can be determined and compared to theoretical calculations.

Similar threads

Proton Structure: De Broglie Wavelength & Resolution
    • Advanced Physics Homework Help
Replies
5
Views
2K
Uncertainty in wavelength and position
    • Advanced Physics Homework Help
Replies
7
Views
2K
B Time Dilation & Muon De Broglie Wavelength: Explained
    • Special and General Relativity
Replies
27
Views
1K
Particle in One-Dimensional Box Problem [Quantum Mechanics]
    • Advanced Physics Homework Help
Replies
3
Views
2K
I De Broglie Wavelength at rest: λ = h/p = h/0 when v=0?
    • Other Physics Topics
Replies
5
Views
1K
De Broglie wavelength of helium atoms
    • Advanced Physics Homework Help
Replies
2
Views
5K
When does the wavefunction wavelength equal the De Broglie wavelength?
    • Quantum Interpretations and Foundations
Replies
2
Views
1K
A De Broglie to Schrödinger to Thomson to Bohm?
    • Quantum Interpretations and Foundations
Replies
3
Views
965
A question related to de Broglie wavelength and the Uncertainty Principle
    • Quantum Interpretations and Foundations
Replies
6
Views
2K
I Maximum acceleration of an alpha particle?
    • Classical Physics
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top