- #1
Jolb
- 417
- 29
My question is this: what is the average speed of atoms released from an oven at some temperature T? For example, in a Stern-Gerlach experiment, hydrogen atoms are emitted from an oven and collimated into a beam by passing them through a slit (and then sent into an inhomogenous magnetic field, but I don't really care about these details for this particular question).
The reason I am confused about this is because my gut instinct would be to estimate this using the old thermodynamic expression for an ideal gas: E = 3/2 kT = 1/2 mv^2 which would imply v=\sqrt{\frac{3kT}{m}}
However, upon cracking open my thermodynamics textbook, it seems as though this is the RMS speed of atoms in a gas, rather than the boring-old average speed. The boring old average speed is found by calculating the expectation value of speed in the Maxwell-Boltzmann distribution, as such:
\langle v \rangle = \int_0^{\infty} v \, f(v) \, dv= \sqrt { \frac{8kT}{\pi m}}
They are very close: the factor of 3 just changes to 8/∏. But which one should I use in a Stern-Gerlach question? Which one would actually be observed in a collimated beam of atoms emitted from an oven at temperature T?
Edit: Just to clarify, even though I am using the symbol v, which is usually reserved for the velocity, here I am referring to the speed, which is equal to the magnitude of the velocity vector. That is to say, v=|v|.
The reason I am confused about this is because my gut instinct would be to estimate this using the old thermodynamic expression for an ideal gas: E = 3/2 kT = 1/2 mv^2 which would imply v=\sqrt{\frac{3kT}{m}}
However, upon cracking open my thermodynamics textbook, it seems as though this is the RMS speed of atoms in a gas, rather than the boring-old average speed. The boring old average speed is found by calculating the expectation value of speed in the Maxwell-Boltzmann distribution, as such:
\langle v \rangle = \int_0^{\infty} v \, f(v) \, dv= \sqrt { \frac{8kT}{\pi m}}
They are very close: the factor of 3 just changes to 8/∏. But which one should I use in a Stern-Gerlach question? Which one would actually be observed in a collimated beam of atoms emitted from an oven at temperature T?
Edit: Just to clarify, even though I am using the symbol v, which is usually reserved for the velocity, here I am referring to the speed, which is equal to the magnitude of the velocity vector. That is to say, v=|v|.
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