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zheka24 [161]
3 years ago
11

If a diffuse gas of atoms is trapped, cooled, and compressed, the de Broglie wavelengths of some atoms can become larger than th

e distance between atoms. The overlap between atoms leads to new states of matter. In one experiment, 87Rb atoms were cooled to 20 nK.
Required:
a. What is their de Broglie wavelength at this temperature?
b. How many times larger is this than the 0.47 nm diameter of the atoms?
Physics
1 answer:
skelet666 [1.2K]3 years ago
7 0

Answer:

a)    λ = 0.5346 10⁻⁹ m,  b)  1.13

Explanation:

a) The wave-particle duality is

       λ = \frac{\hbar }{p}

       

the expression for energy kinetic is

      E = p² / 2m

energy is also related to temperature

      E = \frac{3}{2}  \ kT

we substitute

      p =

     λ =

Rubidium's mass is m = 85 uma

we calculate

     λ =

     λ=

     λ = 0.5346 10⁻⁹ m

 

b) the relationship of the two lengths is

           λ /0.47 nm = 0.53 / 0.47 = 1.13

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