Calculating Jeans mass for a hydrogen cloud with unit conversions

[daleklama]

Homework Statement

It is estimated that a particular diffuse hydrogen cloud has a particle density of 3e7 cm^-3, and the temperature is 150 K.
Calculate Jeans mass.

Homework Equations

Jeans mass is given by: (5kT/GmewM(H))^(3/2) . (3/4∏p)^(1/2)

where k = boltzmanns constant = 1.38e-23
T = temperature in Kelvin = 150K
G = Gravitational constant = 6.673e-11
mew = mean molecular weight = ?
m(H)= mass of gas particles = ?
p = cloud mass density = ?

The Attempt at a Solution

I know I just have to fill in the formula, so it should be simple, but I'm really having trouble calculating the parts of the formula.

I don't have a clue about mean molecular weight OR mass of gas particles, and I THINK the 'cloud mass density' is the number given in the question (3e7 cm^-3) but I don't understand how to convert that to metres (the unit cm^-3 is throwing me off.

I really want to calculate this as accurately as I can, could anyone help please?

Thank you.

 

[tms]

I don't have a clue about mean molecular weight OR mass of gas particles,

You know that the gas is hydrogen, so look it up, keeping in mind that hydrogen gas is H₂.

and I THINK the 'cloud mass density' is the number given in the question (3e7 cm^-3) but I don't understand how to convert that to metres (the unit cm^-3 is throwing me off.

Express the centimeter in meters, then cube it.