Calculating Jean's length for neutral hydrogen cloud

[jmaggio14]

Homework Statement

What is the Jean's length in parsecs for a typical neutral hydrogen cloud, which has a density of n(H I) ~10^8 atoms/(m^3) and a temperature of 100K?

Homework Equations

jean's length = sqrt[(15*K*T)/(4pi*G*u*p)]

where:
'K' is the Boltzmann constant
'T' is the temperature of the cloud
'G' is gravitational constant
'u' is Mu or the mass per particle
'p' is Rho or the density of the cloud

I'm assuming 'u' is the mass of a hydrogen atom in kilograms or 1.67*10^(-27)kg?

The Attempt at a Solution

jean's length = 12160m?
That seems far too small for any plausible answer in astronomy, these are usually measured in parsecs

 

[MarcusAgrippa]

Looks like your units may be wrong. The density you give is atoms/m^3. Scanning the units in the above formula, I think Mu (your u) should be in kg, and the density in the Jeans formula should be kg/m^3. That might give you the additional powers of 10 that you need to get a reasonable answer. Check the units of what you substitute into your formula.

It is good practice always to carry units when substituting. That way, you can check the units of the answer for consistency.