Physics peak wavelength and temperature

1. Oct 24, 2015

ezach1

1. The problem statement, all variables and given/known data
The peak intensity of light from the sun occurs at a wavelength 500nm. Astronomers discover a nearby star X which is the same size and mass as the sun, but has a peak wavelength of half this value. Is X hotter or colder than the sun and by how much?

2. Relevant equations

Wiens law
Max= c/t where c is a constant equal to 2897 and t is the temp in kelvin

3. The attempt at a solution

I know I'm suppose to divide when trying to find out the peak wavelength, but it's given so I'm assuming I have to multiply in order to find the temp except I can't figure out the equation.
Any help would be appreciated.

2. Oct 24, 2015

Staff: Mentor

Hi ezach1, Welcome to Physics Forums.

Write the ratios of the wavelengths using Wein's Law. So
$$\frac{λ_{Sun}}{λ_{Star}} = ~?$$

3. Oct 24, 2015

ezach1

I don't know if you want me to type it out...

=λ250nm?

4. Oct 24, 2015

ezach1

λSun
λStar = λ250nm
Or 2 to one?

5. Oct 24, 2015

Staff: Mentor

Yes, you know that the ratio is two to one. That's fine. But you can also write the ratio of Wien's laws for both, and they must have the same ratio, right? What does that yield for the ratio of temperatures?

6. Oct 24, 2015

ezach1

Not sure what you mean about the ratio for both.
As for the temp, would that just mean that I take the temp from the sun, and divide it in half and that would be the temp of the star? Seems too easy and that's what scares me. I'm desperatly trying to learn this.

7. Oct 24, 2015

ezach1

Please bare with me and have some patience. You wouldn't believe how grateful I am for your help. You have no idea. I really want to learn this.

8. Oct 24, 2015

SammyS

Staff Emeritus
I think gneill is suggesting that you use λSUN = C/TSUN and λSTAR = C/TSTAR.

Then, take the ratio of those expressions together with the given information.

9. Oct 24, 2015

ezach1

hmmm, so do you mean in order for me to express the equation correctly, i must take the ratio of those equations together? or is one sufficient?
Also, I dont know the temp of the star. sorry for the noob questions..

10. Oct 24, 2015

SammyS

Staff Emeritus
The temp of the star is what you need to solve for.

11. Oct 24, 2015

ezach1

You say...then take the ration of those two together...do you mean the sun and the star equation? or the sun/sun equation or the star/star equation?

12. Oct 24, 2015

SammyS

Staff Emeritus
You have two ways to write the ratio of the two wavelengths.

One is direct, the other uses Wien's Law (the right hand side).

Those to ratio should be equivalent, so set them equal. That gives you an equation.

13. Oct 24, 2015

ezach1

Ok,...but why use the direct way? Just want to know..

14. Oct 24, 2015

Staff: Mentor

Because the problem statement gives you information regarding the ratio of the wavelengths for the Sun and star. Thus you can write that ratio directly and know its value.

Then you turn to the Wien law and how it relates wavelength to temperature. The Wien law expression for each body can be set as a ratio, too. You know the wavelength ratio value, so a ratio of the the temperature expressions must have the same value. That will tell you the ratio of the temperatures.

15. Oct 24, 2015

ezach1

ok.. gonna work on it now

16. Oct 24, 2015

ezach1

a little help with this....wiens constanst =c, but how do insert that into the equation? 2.898*10∧3 over the temp in farenhiet, or kelvin?

17. Oct 24, 2015

Staff: Mentor

You could look up Wien's Law and find the definition of the constant...

But it should strike you that such a relationship should deal with absolute values (would a negative temperature make sense in the formula?). Also, if you approach the problem as ratios as suggested, you should find that the constant cancels out and you won't need it at all...

18. Oct 24, 2015

ezach1

Im lost...all i have is the temp of the sun which is 6000k and Wiens constant...I dont think that helps me with solving the temp of the star..

19. Oct 24, 2015

SammyS

Staff Emeritus
We have helped by doing everything short of writing out the solution. Neither of us will do that.

20. Oct 24, 2015

ezach1

thank you..i dont want the answer...im currently working on it. If im correct I should be solving for x which is the temp of the star.
Thanks for your patience and time.