De Broglie wavelength of an atom

In summary, the conversation discusses the DeBroglie wavelength of a particle at temperature T and the DeBroglie wavelength of a helium atom. The formula for the DeBroglie wavelength is λ = h/p where p = mv. The DeBroglie wavelength for a helium atom is proven to be λ = h/√(3mKT) by using the equation mv2/2 = 3/2 KT. The question then arises if the same approach can be used to prove the DeBroglie wavelength of a particle, using the equation mv2/2 = 1/2 KT.
  • #1
Molar
45
19
In my book it is says,
DeBroglie wavelength of a particle at temp T is, λ = h/√(2mKT) and
DeBroglie wavelength of He atom is, λ = h/√(3mKT)

Well, λ = h/ mv and mv2/2 = (3/2) KT and so , λ = h/√(3mKT)
How to prove the first one..??
and why they are different...??
 
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  • #2
Try and follow the format for asking HW questions.
 
  • #3
Sorry for that...being new I didn't get it ...
Here it is..

Homework Statement

Prove that , DeBroglie wavelength of a particle at temp T is, λ = h/√(2mKT) and
DeBroglie wavelength of He atom is, λ = h/√(3mKT)
h = Planck's constant ; K = Boltzmann constantRelevant equations

λ = h/p ,
p = mv ,
mv2/2 = 3/2 KT


The attempt at a solution

For helium atom we take
mv2/2 = 3/2 KT
so, v = √ (3KT/m)
∴ λ = h/√(3mKT) ...(proved)

My question is for the deBroglie wavelength of a particle should I take
mv2/2 = 1/2 KT and proceed like before...??
 

1. What is the De Broglie wavelength of an atom?

The De Broglie wavelength of an atom is a concept in quantum mechanics that describes the wave-like behavior of matter. It is the wavelength associated with the motion of a particle, and is given by the equation λ = h/mv, where h is Planck's constant, m is the mass of the particle, and v is its velocity.

2. How is the De Broglie wavelength related to an atom's momentum?

The De Broglie wavelength is inversely proportional to an atom's momentum. This means that as the momentum of an atom increases, its De Broglie wavelength decreases. Conversely, as the momentum decreases, the De Broglie wavelength increases.

3. Can the De Broglie wavelength of an atom be measured?

Yes, the De Broglie wavelength of an atom can be measured using specialized techniques such as electron diffraction or neutron interferometry. These techniques involve measuring the interference patterns produced by the atom's wave-like behavior.

4. What is the significance of the De Broglie wavelength of an atom?

The De Broglie wavelength is significant because it provides insight into the wave-particle duality of matter. It demonstrates that all matter, including atoms, can exhibit both wave-like and particle-like behavior. This concept is crucial to understanding the behavior of particles at the atomic and subatomic level.

5. How does the De Broglie wavelength of an atom differ from that of larger objects?

The De Broglie wavelength of an atom is significantly smaller than that of larger objects, such as a baseball or a person. This is because the De Broglie wavelength is inversely proportional to an object's mass, so the smaller the mass, the larger the wavelength. Therefore, the De Broglie wavelength of an atom is only observable at the atomic level and cannot be detected in everyday objects.

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