Most Probable Speed - Atoms From An Oven

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SUMMARY

The discussion focuses on calculating the most probable speed of aluminium atoms ejected from an oven at a temperature of 900°C (1173.15K). The formula used is vmp=√(2kT/m), where k is the Boltzmann constant. The correct value for the Boltzmann constant in SI units is 1.38e-23 J/K. By substituting the molar mass of aluminium (0.027 kg/mol) and converting it to the mass of a single molecule, the calculated velocity aligns with the expected range of hundreds of meters per second.

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  • Understanding of the ideal gas law and kinetic theory of gases
  • Familiarity with the Boltzmann constant and its units
  • Knowledge of molar mass and Avogadro's number
  • Basic algebra for manipulating equations
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bobbles22
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Hi there,

I'm looking to find the most probable speed of atoms ejected from an oven.

Temp (T) is 900°C (so 1173.15K).

The material is aluminium with molar mass 0.027kg mol-1

I've got the formula vmp=√(2kT/m)

I'm fine with everything above, but I'm not sure what value to use as the Boltzmann constant k.

Can anyone please help me here? Do I have the right equation and what value for the constant should I use (sounds silly, but it changes depending upon units. I've tried a couple but get silly tiny speeds out. I think I should expect something in the region of a few hundred metres per second).

Many thanks

Bob
 
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In SI units:
K = 1.38e-23 J/K
m = mass of one molecule = 0.027/6.022e23 kg
T = 1173 K

... which gives a velocity of "hundreds of m/s" as you expected.
 

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