Spectral types and luminosity?

Question

A population of stars is born that has the following number of each type of Main Sequence star:

O = 5, B = 20, A = 30, F = 50, G = 75, K = 750, M = 2250

The mass of a typical star in each spectral type (where the units are in solar masses, that is, the Sun's mass = 1) is approximately:

O = 30, B = 6, A = 3, F = 2, G = 1, K = 0.5, M = 0.2

In this population of stars, which spectral type contributes the largest percentage of the total mass of the entire population?

Estimate the average luminosity for each of these spectral types of Main Sequence stars from one of the many HR diagrams in your textbook or in the lessons. Which spectral type contributes the largest percentage of the total luminosity of the entire population?

Answer 1

Maybe I'm dumb, but it seems to me that you would multiply, for each spectral type, the number of stars times the mass to get the total mass for that spectral type.  Then whichever spectral type comes up with the highest number would have the largest percentage of the mass for the entire group.  

i.e.  

for O type 5 x 30 = 150 solar masses  

for B type 20 x 6 = 120 solar masses

and so on and so forth  

And I missing something here?

Answer 2

i had to take this shiat too..

im sorry i have no idea,

try looking on science or astronomy websites or on the index in your textbook thats what i would do

good luck

Answer 3

It is an arithmetic problem:

The mass of all O stars is

5 stars times 30 units per star = 150 units

for all B stars:

20 stars times 6 units per star = 120 units

etc.

The spectral class that has the biggest percentage of mass is the class with the biggest total of units (at first glance, looks like M).

Next, go to the HR diagram.  Look up the luminosity value for each spectral class (usually given in solar luminosities).

Do the same thing (luminosity is additive so you are doing exactly the same exercise)

for O class

5 stars at 1000 units each = 5000

for B class:

20 stars at 500 units each = 10,000

etc.  (except you should use a better graph than mine and use the values it shows)

One class will have a bigger luminosity total than the others.  That's the winner.  Usually around B or A in real life.

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The moral of the story is:

when we look at the universe, it is much easier to see the very bright star, but they do not represent the majority.

Most of the stars that we see with our eyes are O B A F (which goes well with the calculation you will have done above)

but we know (also from above) that the majority of stars are G K and specially M

Our own Sun (G type) would not be visible with naked eyes, at a distance of 50 light-years, which is an extremely small distance in astronomy -- the Galactic centre is 25,000 light-years away and the nearest large spiral galaxy like ours is over two million light-years away.

K and M are fainter than G.