- #1

cyberdeathreaper

- 46

- 0

For what temperatures are the atoms in an ideal gas at pressure [itex] P [/itex] quantum mechanical?

*Hint:*Use the idea gas law

[tex]

PV = N k_B T

[/tex]

to deduce the interatomic spacing.

*Answer:*

[tex]

T < \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left( \frac{3}_{5} \right)} \left( P^\frac{2}_{5} \right)

[/tex]

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Now, I have been given the formula for the typical de Broglie wavelength:

[tex]

\lambda = \frac{h}_{\sqrt{3 m k_B T}}

[/tex]

Further, I know I am trying to determine when

[tex]

\lambda > d

[/tex]

where

*d*is the interatomic spacing.

However, what I don't understand is how I can calculate a value for

*d*given the idea gas law in the question. Any ideas?