Speed of atoms ejected from an oven

In summary: This will give you a higher average speed, since the particles that are travelling faster will outnumber the slower ones.
  • #1
Jolb
419
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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 [tex]v=\sqrt{\frac{3kT}{m}}[/tex]
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:
[tex]\langle v \rangle = \int_0^{\infty} v \, f(v) \, dv= \sqrt { \frac{8kT}{\pi m}} [/tex]
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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  • #2
The second one.
 
  • #3
The second one does seem more obvious, but why does my "gut instinct" derivation fail? It seems to me that if we know some expression for the average kinetic energy (E=3/2 kT), the expression should give the average speed, not the RMS speed. Why does that derivation give RMS rather than the correct answer?

Also, references would be appreciated.
 
  • #4
Depends what you are deriving and how you go about it.

The rms velocity is what you get in the first one because the particles in the gas are equally likely to be heading an any direction - giving an average velocity of zero. You can see why this is not useful.

Put a hole in the walls though, and you are selecting for those particles that are headed in a subset of possible directions.
 
  • #5


Thank you for your question. The average speed of atoms ejected from an oven at temperature T can be calculated using the Maxwell-Boltzmann distribution, as you have correctly stated. This distribution takes into account the statistical distribution of speeds among a large number of particles in a gas. Therefore, it would be more appropriate to use this distribution to estimate the average speed of atoms in a collimated beam emitted from an oven at temperature T. This is because the Maxwell-Boltzmann distribution takes into account the variation in speeds among the atoms, rather than just the root-mean-square (RMS) speed.

In a Stern-Gerlach experiment, the atoms are emitted from an oven and then collimated into a beam. This means that the atoms in the beam will have a range of speeds, and the Maxwell-Boltzmann distribution can give us an estimate of the average speed of the atoms in this beam. However, as you have also mentioned, the inhomogeneous magnetic field in the experiment can affect the trajectory of the atoms and their final speed. Therefore, the calculated average speed may not exactly match the observed speed in the experiment.

In summary, for your particular question, it would be more appropriate to use the Maxwell-Boltzmann distribution to estimate the average speed of atoms in the collimated beam emitted from the oven at temperature T. However, the actual observed speed may vary due to other factors such as the inhomogeneous magnetic field in the Stern-Gerlach experiment. It is important to consider all these factors when interpreting the results of an experiment.
 

1. How is the speed of atoms ejected from an oven measured?

The speed of atoms ejected from an oven is typically measured using a technique called time-of-flight (TOF) spectroscopy. This involves measuring the time it takes for the atoms to travel a known distance and using this information to calculate their speed.

2. What factors affect the speed of atoms ejected from an oven?

The speed of atoms ejected from an oven can be affected by a variety of factors including the temperature of the oven, the type of atoms being ejected, and the pressure inside the oven. Additionally, the shape and design of the oven can also impact the speed of ejected atoms.

3. Can the speed of atoms ejected from an oven be controlled?

Yes, the speed of atoms ejected from an oven can be controlled by adjusting the temperature, pressure, and/or design of the oven. This can be useful for specific experiments or applications that require atoms to be ejected at a specific speed.

4. Why is the speed of atoms ejected from an oven important?

The speed of atoms ejected from an oven is important because it can provide valuable information about the properties and behavior of the atoms being ejected. It can also be used to study and manipulate chemical reactions, as well as to create and study new materials.

5. How does the speed of atoms ejected from an oven relate to the Kinetic Theory of Gases?

The Kinetic Theory of Gases states that the average kinetic energy of gas particles is directly proportional to their temperature. This means that as the temperature of the oven increases, the speed of atoms ejected from it will also increase. Additionally, the speed of ejected atoms can also provide insights into the distribution of kinetic energy among the atoms in the oven, which is a key concept in the Kinetic Theory of Gases.

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