Dark interstellar gas clouds contain so many dust grains that starlight cannot pass through, even though the dust grains are tiny and the spaces between them are quite large by earthly standards. A typical dust grain has a radius of about 1.00*10^-7 meter and a mass of about 1.00*10^-14 gram.
A) Estimate how many dust particles there are in a cloud containing 1.50×10^3 Msun of dusty gas, if 1.6% of the cloud's mass is in the form of dust grains.
B) Estimate the total surface area these grains would cover if you could put them side by side. You can assume that the grains are approximately spherical so that each grain covers an area pir^2 where r is the grain's radius. State your answer in square light-years.
C) Estimate the total surface area the cloud covers, assuming that its matter density is like that of a typical molecular cloud,about 10^-21 g/cm^3 . (Hint: First calculate the cloud’s volume from its mass and density, then determine the cloud’s radius using the formula for the radius of a sphere R = (3 x volume/4)^1/3.) State your answer in square light-years.
Err has anyone done a question like this before??? For A) I got 3*10^50 dust grains...which seems completely wrong, could use a tip or two. Thanks.
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