Simple De Broglie Wavelength Problem

In summary, the De Broglie wavelength of a proton with a kinetic energy of 10 eV is 12.2 nm, which is incorrect. The correct formula is \lambda = \frac{hc}{pc}, where hc = 1239.8 nm*eV and pc = \sqrt{{KE}^2 + 2KEm_0c^2}. The mistake may have been due to confusion between MeV and eV.
  • #1
vsage
I have the formula for the de Broglie wavelength but for some reason I'm not using it properly. Here's the question:

What is the De Broglie wavelength (in nm) of a proton with a kinetic energy of 10 eV? (Take the mass of a proton to be 938 MeV/c2.)

[tex]\lambda = \frac{hc}{pc}[/tex]

hc = 1239.8 nm*eV
[tex]pc = \sqrt{{KE}^2 + 2KEm_0c^2}[/tex] which should be around 101.5 eV, so the answer would be 12.2nm which is wrong! What did I do wrong? It should have been a simple plug and chug problem after deriving pc in terms of KE and the rest mass.
 
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  • #2
Nevermind! Apparently in my crazy mind 0.511MeV = 511eV
 
  • #3
What would you need that number?

Daniel.
 

1. What is the De Broglie wavelength?

The De Broglie wavelength, also known as the matter wavelength, is a concept in quantum mechanics that describes the wavelength of a particle. It is named after French physicist Louis de Broglie, who proposed that all particles, including matter, have a wave-like nature.

2. How do you calculate the De Broglie wavelength?

The De Broglie wavelength can be calculated using the formula λ = h/mv, where λ is the wavelength, h is the Planck's constant, m is the mass of the particle, and v is its velocity. This formula is based on the wave-particle duality principle, which states that particles can exhibit both wave-like and particle-like behavior.

3. What is the significance of the De Broglie wavelength?

The De Broglie wavelength is significant because it helps us understand the behavior of particles at the quantum level. It allows us to describe the wave-like properties of particles and also explains phenomena such as diffraction and interference, which are typically associated with waves.

4. Can the De Broglie wavelength be observed?

No, the De Broglie wavelength cannot be directly observed because it is a property of particles at the quantum level. However, its effects can be observed in experiments, such as the double-slit experiment, where the interference pattern of particles can be seen.

5. How does the De Broglie wavelength relate to the uncertainty principle?

The De Broglie wavelength is closely related to the Heisenberg uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. The De Broglie wavelength is inversely proportional to the momentum of a particle, so as the uncertainty in momentum increases, the uncertainty in the De Broglie wavelength also increases.

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