The intensity of light from a star (its brightness) is the power it outputs divided by the surface area over which it’s spread: i = p 4πd2 . suppose two stars of the same apparent brightness i are also believed to be the same size. the spectrum of one star peaks at 750 nm while the other peaks at 450 nm. use wien’s law and the stefan-boltzmann equation to estimate their relative distances from u

Explanation:

1. We can find the temperature of each star using the Wien's Law. This law is given by:

(1)

So, the temperature of the first and the second star will be:

Now the relation between the absolute luminosity and apparent brightness  is given:

(2)

Where:

Now, we know that two stars have the same apparent brightness, in other words l₁ = l₂

If we use the equation (2) we have:

So the relative distance between both stars will be:

(3)

The Boltzmann Law says, (4)

Let's put (4) in (3) for each star.

As we know both stars have the same size we can canceled out the areas.

I hope it helps!

b

explanation: