Is the Cloud of Hydrogen Gas Likely to Collapse?

[Meganwright]

Homework Statement

A cloud consists of 8 solar masses of hydrogen gas (H2). Its temperature is 20 K and its radius is 0.6 light years. Will it collapse?

Homework Equations

jeans mass


3. The Attempt at a Solution [/b
I've tried to use jeans mass to solve this however I am finding the formula difficult to understand

 

[vela]

Show your work.

 

[Meganwright]

So far I'm using the formula
3/2kT <GMm/R
And (3KT/2Gm) x k >mj

I'm substituting m=2.167x10^-27
G=6.67x10^-11
K=1.38x10^-23
T=20
R=0.6

However I'm not sure what it is exactly that I'm gaining from using these formulae?
I'm getting that (3kT/2Gm) x R = 1.115011357 x 10^15 ?
I'm aiming to get an answer of
Jeans mass = 1.05 x 10^31 kg
Which is less than 8 solar masses (1.6 x 10 ^31) so it will collapse?

 

[haruspex]

I struggled to follow your logic above. Seem to be a few typos:

(3KT/2Gm) x k >mj

(3kT/2Gm) x R = Mj ?

(3kT/2Gm) x R = 1.115011357 x 10^15

√((3kT/2Gm) x R) = 1.115011357 x 10^15 ?
Also, I don't see online a formula with that 3/2 factor. I see one with 15/4pi, another that approximates that to 1. Anyway, using your 3/2 I get that the Jeans length/radius = 0.84, which suggests to me it won't collapse. (I'm a bit confused over whether the Jeans length is a radius or a diameter, but if it's a diameter then the actual radius is much too large to collapse.)