Astrophysics - Temperature of a star via flux and wavelength

[cwolfx2]

Homework Statement

What is the temperature of a star if the flux at 450 nm is measured to be 1.3 times the flux at 650 nm.

Homework Equations

I tried to use the equation Flux = 2πhv³/c²

e^x-1
x= hv/kt

making 2 of the equations equal each other and solve for T. However being out of practice for months now i do not remember what e represents and how to solve for an exponent.

Though I imagine I may have the wrong equation and not sure if i need to or how to incorporate the wavelengths.

 

[cepheid]

What is the temperature of a star if the flux at 450 nm is measured to be 1.3 times the flux at 650 nm.

Homework Equations

I tried to use the equation Flux = 2πhv³/c²

e^x-1
x= hv/kt

Your spacing wasn't preserved, but if you meant

$$F(\nu, T) = \frac{2\pi h\nu^3/c^2}{e^{h\nu/kT} - 1}$$

then yes, this is Planck's law for blackbody radiation.

making 2 of the equations equal each other and solve for T. However being out of practice for months now i do not remember what e represents and how to solve for an exponent.

'e' is just a number. Granted, it's an irrational number, and it is often used as a base for exponentials because an exponential function with e as a base has certain special properties that are convenient.

In order to solve for x, you have to undo the raising of e to the power of it. In other words, you have to do the inverse operation of taking an exponential. That inverse operation is taking the logarithm to base e, which is also known as the natural logarithm.

Though I imagine I may have the wrong equation

Modelling the star as an ideal blackbody radiator seems like a reasonable approach.

and not sure if i need to or how to incorporate the wavelengths.

Of course you need to incorporate them. The Greek symbol 'nu' ($\nu$) in Planck's law represents frequency. What is the relationship between frequency and wavelength?

 

[cwolfx2]

Apologies for not getting back sooner, I had the wrong email attached to this account. Thanks for the response, I feel silly on some of my oversights such as e (need to look on my calculator more).