Rms speed of Hydrogen atoms in space

In summary, in outer space the density of matter is about one atom per cm^3, mainly hydrogen atoms, with a temperature of 2.7 K. To calculate the rms speed of these atoms and the pressure in atmospheres, we can use the equation PV = NkT, where P is pressure, V is volume, N is number of atoms, k is Boltzmann's constant, and T is temperature. However, we are missing the volume variable. We can use the equipartition theorem, which states that hydrogen atoms have a kinetic energy of 3/2kT due to their 3 degrees of freedom. Using this, we can solve for the mass of the hydrogen atoms by setting 1/
  • #1
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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  • #2
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.
 
  • #3
Ok...so 1/2(mv^2)=3/2kT. But what do I use for mass?
 

1. What is the Rms speed of Hydrogen atoms in space?

The root mean square (Rms) speed of Hydrogen atoms in space is approximately 10.8 kilometers per second. This is the average speed of Hydrogen atoms in a gas or plasma at a given temperature.

2. How is the Rms speed of Hydrogen atoms in space calculated?

The Rms speed of Hydrogen atoms in space is calculated using the root mean square formula, which takes into account the velocities of all the atoms in a given sample. For Hydrogen atoms in space, this calculation is based on the Maxwell-Boltzmann distribution.

3. Why is the Rms speed of Hydrogen atoms in space important?

The Rms speed of Hydrogen atoms in space is important because it provides information about the temperature and energy of the gas or plasma in which the atoms are moving. It is also a key factor in understanding the processes and dynamics of interstellar gas clouds.

4. Does the Rms speed of Hydrogen atoms in space vary in different regions of space?

Yes, the Rms speed of Hydrogen atoms in space can vary depending on the environment. For example, in the cold, dense regions of interstellar clouds, the Rms speed may be significantly lower than in the hotter, more diffuse regions.

5. How does the Rms speed of Hydrogen atoms in space compare to other elements?

The Rms speed of Hydrogen atoms in space is generally lower than that of other elements due to its smaller mass. Heavier elements typically have higher Rms speeds at the same temperature. However, this can vary depending on the specific conditions and environment in which the atoms are located.

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