# Hydrogen in space

## Homework Statement

in space far from stars is filled with a very low density of hydrogen atoms, the number density is about 1atom/cm^3 and T is about 3degreeK

a. estimate the pressure in space, answer in Pa and atm.
b. what is the rms speed of the atoms
c. what is the edge length L of an LxLxL cube of gas with 1J of thermal energy
k=1.38x106-23
1atm=101.3kPa
atomic mass of hydrogen=1.67x10^-27kg

N/V=n
vrms=sqrt(3kT/m)
N/V*M=m
PV=NkT

## The Attempt at a Solution

a. P=(N/V)kT=(1/1x10-6)*1.38x10^-23*3=4.14x10^-17Pa=4x10^-22atm?
b.m=(N/V)M=(1/1x10^-6)1.67x10^-27=1.67x10^-22kg
so vrms=sqrt(9*1.38x10^-23/1.67x10^-22)=.86m/s????

and c. i have no idea, plz someone help, this micro macro stuff is stupid.... im not sure about the vrms formula is correct, since in the book it says its for molecules, but i cant find anything on atoms... im pretty sure i have done something wrong for the number density, as i dont know, coz its in atoms/cm^3.... and im just stuck plz some help me...

ok well i think m is just atomic mass so vrms=sqrt(9*1.38x106-23/1.67x10^-27)=273m/s i think
plz can anyone tell me if i am doing this right?????

alphysicist
Homework Helper
Hi fredrick08,

What is the average kinetic energy of one atom? And so how many atoms would you need to give 1 J of energy? Once you have that, how is the number of atoms related to the volume they occupy?

How about just converting to moles per volume? A gas is 22.4 liters per mole at STP. Just use the gas laws from chemistry.

alphysicist
Homework Helper
Hi sirzerp,

Perhaps I'm not understanding your train of thought; how will converting to moles and calculating volumes at STP help find the volume containing 1 J of energy at 3K?

Redbelly98
Staff Emeritus
Homework Helper
(a) looks good to me

(b)
vrms=sqrt(9*1.38x106-23/1.67x10^-27)

Right idea, but one of the numbers is incorrect here.

Hi sirzerp,

Perhaps I'm not understanding your train of thought; how will converting to moles and calculating volumes at STP help find the volume containing 1 J of energy at 3K?

We know the number of moles per volume and temp. Just treat it as an ideal gas right?

Once you know pressure, is not pressure a direct energy unit?

Last edited:
alphysicist
Homework Helper
Hi Redbelly98,

(a) looks good to me

(b)

Right idea, but one of the numbers is incorrect here.

There is a 6 where a ^ should be; but I think other than that the numbers are correct. Are you seeing something that I am overlooking?

alphysicist
Homework Helper
We know the number of moles per volume and temp. Just treat it as an ideal gas right?

Once you know pressure, is not pressure a direct energy unit?

Yes, so you could use

$$P =\frac{2}{3}\frac{U}{V}$$

and solve for V; but I don't think you need to convert to moles or calculate things at STP.

-------------------

My original suggestion also gave the volume in two step from the given data. The number of molecules giving an energy U is:

$$U=\frac{3}{2} N k T$$

and since the density is (1 atom/cm^3) then number for N is the volume (in cm^3).

Redbelly98
Staff Emeritus
Homework Helper
There is a 6 where a ^ should be; but I think other than that the numbers are correct. Are you seeing something that I am overlooking?

Oops, I was looking at the first factor of 9, thinking it should be a 3. But he had already multiplied 3 with the T=3K.

Sorry! (b) looks good to me now!

ok ty heaps, srry i was away, just got up lol, ok it makes sense now, srry for also confusing anyone, unfortunately ive never done chemistry before, so i dont really know the chem formulas just the ones in my physics book...