Question

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

Answer 1

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