Calculating the monochromatic flux of a star

[Chowie]

Homework Statement

A star has a photospheric temperature of 5000 K, a radius of 0.9Ro, (Ro = radius of sun). If the star is 20 pc away, calculate the monochromatic flux (In Wm^2micron^-1) at 500 nm, measured at Earth.

Calculated the surface area to be 1.6416*10^18 m^2.

Homework Equations

We were given this hint: The plank curve gives the monochromatic surface flux and is:

where Beta was given to us as 2*pi*h*c^2. with k being the Boltzmann constant, h being the Planck constant and c the speed of light

The Attempt at a Solution

I calculated the monochromatic surface flux to be 3.773*10^13 Wm^-3 and 2.358*10^-12 W m^-2 micrometres^-1 (These are the units for straight monochromatic flux, I'm just guessing here, I'm pretty sure they're not the same) however I have no idea how to convert this into straight monochromatic flux. My friend thinks another solution is to calculate the bolometric flux and then convert it into monochromatic, any suggestions?

EDIT: Another possible solution might be to do with combining the surface area and surface flux in some manner, however I do not know the units for surface flux and there isn't much literature about it ( the first result in google for monochromatic surface flux is this post >_>)

 

[darkys]

Any help would be greatly appreciated! EDIT: I have managed to calculate the monochromatic flux by multiplying the surface area by the monochromatic surface flux, I calculated it to be 5.844*10^-3 Wm^-2micron^-1. Is this right?