De Broglie wavelength of an atom

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SUMMARY

The discussion centers on the derivation of the De Broglie wavelength formulas for particles at temperature T, specifically highlighting the differences between a general particle and a helium atom. The formula for a general particle is given as λ = h/√(2mKT), while for a helium atom, it is λ = h/√(3mKT). The derivation for the helium atom is confirmed using the kinetic energy expression mv²/2 = (3/2)KT. The user seeks clarification on whether to use mv²/2 = (1/2)KT for the general particle derivation.

PREREQUISITES
  • Understanding of De Broglie wavelength
  • Familiarity with Planck's constant (h) and Boltzmann constant (K)
  • Basic knowledge of kinetic theory of gases
  • Ability to manipulate equations involving mass (m) and temperature (T)
NEXT STEPS
  • Study the derivation of the De Broglie wavelength for various particles
  • Explore the implications of temperature on particle behavior in quantum mechanics
  • Learn about the kinetic theory of gases and its relation to molecular speeds
  • Investigate the differences in behavior between monoatomic and diatomic gases
USEFUL FOR

Students and educators in physics, particularly those focusing on quantum mechanics and statistical mechanics, as well as anyone interested in the behavior of particles at different temperatures.

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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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Try and follow the format for asking HW questions.
 
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...??
 

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