Typical molecular clouds have a temperature of 32.0 K and a particle density of 300 per cubic centimeter.?

Question

Estimate how large the radius of a molecular cloud with this temperature and density needs to be for the cloud to harbor star formation. Give your answer in both meters and light-years. (For the purposes of this estimate, you can assume the cloud is perfectly spherical with a volume 4(3.14)r^3/3 and that it is made entirely of hydrogen molecules of mass 3.30×10^-24g)

I switched the question and the given info because there wasn't enough room for the question. I have an answer but wanted to be sure before submitting it.

Answer 1

For a star to form, you need a very high temperature to start fusion (~10^7 K). No matter how big your cloud is, if it's temperature is 32K, you are never going to start fusion.

Answer 2

The minimum mass that is needed depends on the metallicity and is estimated to be about 50 to 100 times the mass of Jupiter. Your pure hydrogen cloud would be at the high end.

Now for the calculations: 100 times the mass of Jupiter is 100 x 2 x 10^27 = 2 x 10^29 kg. (about 10% of the mass of the Sun).

1 hydrogen molecule has a mass of 3.34 x 10^-27 kg. Divide the two to find that we need 6x10^55 molecules.

Divide by the density of 1.1 x 10^5 particles/cm^3 to get 5.4 x 10^50 cm^3.

Such a volume corresponds to a radius of 5.1 x 10^16 cm or about 3000 AU.