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. Participants utilize the ideal gas law, PV = NkT, and the equipartition theorem to derive the kinetic energy of hydrogen atoms, which is expressed as 3/2kT due to their three degrees of freedom. The challenge arises in determining the mass of hydrogen atoms for the calculation of rms speed.

PREREQUISITES
  • Understanding of the ideal gas law (PV = NkT)
  • Familiarity with the equipartition theorem
  • Knowledge of kinetic energy equations (1/2 mv²)
  • Basic concepts of atomic mass (mass of hydrogen atoms)
NEXT STEPS
  • Calculate the rms speed of hydrogen atoms using the derived equations
  • Research the mass of hydrogen atoms for accurate calculations
  • Explore the implications of temperature on atomic speed in gases
  • Investigate the relationship between pressure and atomic density in space
USEFUL FOR

Students in physics or chemistry, educators teaching thermodynamics, and anyone interested in astrophysics or the behavior of gases in 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

PV = NkT




The Attempt at a Solution

So by using PV = NkT, I have all the variables except the volume. Or am I way off using this equation.
 
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Have you encountered the equipartition theorem before? According to the theorem, hydrogen atoms have a kinetic energy of 3/2kT, because they have 3 degrees of freedom.
 
Ok...so 1/2(mv^2)=3/2kT. But what do I use for mass?
 

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