RMS speed of Hydrogen Atoms in space

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SUMMARY

The discussion focuses on calculating the root mean square (rms) speed of hydrogen atoms in outer space, where the density is approximately one atom per cm³ and the temperature is 2.7 K. The relevant equation used is 0.5mv² = 3/2 KT, which can be rearranged to vrms = √(3RT/M), where R is 8.3145 kg m²/s²-mol-K and M is the molecular mass of hydrogen (1.0079 atomic mass units). Participants emphasize the importance of converting the molecular mass into appropriate units for accurate calculations.

PREREQUISITES
  • Understanding of the ideal gas law and kinetic theory of gases
  • Familiarity with the concept of root mean square speed
  • Knowledge of unit conversions, particularly for molecular mass
  • Basic proficiency in algebra for manipulating equations
NEXT STEPS
  • Learn about the ideal gas law and its applications in astrophysics
  • Study the derivation of the rms speed formula in kinetic theory
  • Explore the properties of hydrogen and its molecular mass calculations
  • Investigate the implications of temperature on gas behavior in space
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Students in physics or chemistry, educators teaching kinetic theory, and researchers interested in the behavior of gases in low-density environments such as outer space.

notsam
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Homework Statement

In outer space the density of matter is about one atom per cm^3, mainly hydrogen atoms , and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).






Homework Equations

.5mv^2 = 3/2 KT



The Attempt at a Solution

PLEASE HELP! :) Ok so I have all knowns EXCEPT mass to I get that from my density? Using whatever hydrogens molecular mass is?
 
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notsam said:

Homework Equations

.5mv^2 = 3/2 KT

The Attempt at a Solution

PLEASE HELP! :) Ok so I have all knowns EXCEPT mass to I get that from my density? Using whatever hydrogens molecular mass is?

I use a variation of the formula in my teaching. Oxtoby, Gillis and Nachtrieb have a good derivation. I'm not sure if http://books.google.com/books?id=kX...onepage&q=the meaning of temperature&f=false" will work for you. If not, search Google Books for the authors. The text is Principles of Modern Chemistry. It is on page 379 of the sixth edition.

It ends with vrms=\sqrt{3RT/M}
where R = 8.3145 kg m2/s2-mol-K
and M is the molecular mass in kg/mol

I am pretty sure the equation you gave will work using the mass of H (1.0079 atmic mass units) in the appropriate units.
 
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