# Initial mass function problem

1. Oct 26, 2009

### kranav

1. The problem statement, all variables and given/known data

the question says, consider a newly formed globular cluster, with a total mass 10^6 times mass of the sun and an initial mass function dN/dm = a.m^-2.35 in the mass range 0.1 - 20 times mass of the sun, where m = M/mass of the sun.
find the constant a. (answer : 1.9 x10^5)
thanks.

2. Relevant equations

3. The attempt at a solution

the number of stars in a globular cluster are between 10^4 - 10^6. but N from the above equation should be smaller as the mass range is from 0.1 to 20 times sun's mass. If I can find that N the equation is a piece of cake.

2. Oct 26, 2009

### gabbagabbahey

3. Oct 26, 2009

### kranav

I'm really sorry about that ... wasn't aware of that. I thought if I could reframe the question and start afresh

4. Oct 26, 2009

### gabbagabbahey

After looking up "initial mass function", it looks like the number of stars in the mass range $m_0$ to $m_1$ is given by

$$N=\int_{m_0}^{m_1}\frac{dN}{dm}mdm$$

Have you tried performing this integration?

5. Oct 26, 2009

### kranav

Yes this time I got it. Thank you very much