cyberdeathreaper
Apr26-05, 05:36 PM
Here's the question:
For what temperatures are the atoms in an ideal gas at pressure P quantum mechanical?
Hint: Use the idea gas law
PV = N k_B T
to deduce the interatomic spacing.
Answer:
T < \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left( \frac{3}_{5} \right)} \left( P^\frac{2}_{5} \right)
-------------
Now, I have been given the formula for the typical de Broglie wavelength:
\lambda = \frac{h}_{\sqrt{3 m k_B T}}
Further, I know I am trying to determine when
\lambda > d
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?
For what temperatures are the atoms in an ideal gas at pressure P quantum mechanical?
Hint: Use the idea gas law
PV = N k_B T
to deduce the interatomic spacing.
Answer:
T < \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left( \frac{3}_{5} \right)} \left( P^\frac{2}_{5} \right)
-------------
Now, I have been given the formula for the typical de Broglie wavelength:
\lambda = \frac{h}_{\sqrt{3 m k_B T}}
Further, I know I am trying to determine when
\lambda > d
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?