Physics peak wavelength and temperature

[ezach1]

Homework Statement

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?[/B]

Homework Equations

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

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. [/B]

 

[gneill]

Hi ezach1, Welcome to Physics Forums.

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

 

[ezach1]

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

=λ250nm?

 

[ezach1]

λSun
λStar = λ250nm
Or 2 to one?

 

[gneill]

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?

 

[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.

 

[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.

 

[SammyS]

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 desperately trying to learn this.

I think gneill is suggesting that you use λ_SUN = C/T_SUN and λ_STAR = C/T_STAR.

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

 

[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 don't know the temp of the star. sorry for the noob questions..

 

[SammyS]

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 don't know the temp of the star.

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

 

[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?

 

[SammyS]

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?

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.

 

[ezach1]

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

 

[gneill]

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

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.

 

[ezach1]

ok.. going to work on it now

 

[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?

 

[gneill]

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?

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...

 

[ezach1]

Im lost...all i have is the temp of the sun which is 6000k and Wiens constant...I don't think that helps me with solving the temp of the star..

 

[SammyS]

Im lost...all i have is the temp of the sun which is 6000k and Wiens constant...I don't think that helps me with solving the temp of the star..

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

 

[ezach1]

thank you..i don't want the answer...im currently working on it. If I am correct I should be solving for x which is the temp of the star.
Thanks for your patience and time.

 

[SammyS]

thank you..i don't want the answer...I'm currently working on it. If I'm correct I should be solving for x which is the temp of the star.
Thanks for your patience and time.

Show us that equation with x in it.

 

[ezach1]

I will post my answer in a bit and will continue to work. Thanks again

 

[ezach1]

2.898/6000k = 2.898/x

 

[SammyS]

2.898/6000k = 2.898/x

No.

That simply gives x = 6000 K.

 

[SammyS]

Try another approach.

Solve Wiens Law for C

 

[ezach1]

5x10^5=0.0029/T

 

[ezach1]

λ=b/t
250nm=0.028977 mK/T

 

[SammyS]

5x10^5=0.0029/T

I was thinking more along the lines:

Wien's Law: λ_max = C/T

Solving for C gives:

C = T⋅λ_max​

Added in Edit:

Can you see how this might help you solve your problem ?

 

[ezach1]

ok, working on this equation now..

As for the other parts of the question...

Nus is discovered to have eight planets in orbit. These eight planets are separated from Nus at precisely the same distances as the planets in our own Solar System are from the Sun. Do you expect that this system will be comprised of greater, fewer or the same number of giant planets as the Solar System, and why? [6 pts] c) The third planet from Nus, Htrae, has a single large moon, Noom. Astronomers learn that the Noom has a low density, has plenty of volatiles and that Htrae is spinning extremely rapidly. Based on this information, what is the most favorable hypothesis explaining the origin of Noom?

I would say that the system will be comprised of the same number as the solar system due to the fact the gas giants would be beyond the frostline where the suns heat would start to diminish, kind of like in our solar system. The heavier elements like rock and metal will stay inside the frost line and that might even lead to more terrestrial-like planets in Nus' system, but the lighter elements like hydrogen and helium are captured by the planets with enough mass to do so outside of the frostline.
Anyone want to correct me?
Noom has a lower density because the impact of giant protoplanetary collision gouged out the outer crust and mantle, and didn’t eject so much of the Htrae's iron core.The huge cloud of ejected debris coalesced into the Noom. The object that collided with Htrae mustve been huge and abundant in volatiles, hence the traces in its composition.
Is it safe to say the fast spinning of Htrae has to do with the the size of the object that collided with it?

 

[SammyS]

ok, working on this equation now..

As for the other parts of the question...

Nus is discovered to have eight planets in orbit. These eight planets are separated from Nus at precisely the same distances as the planets in our own Solar System are from the Sun. Do you expect that this system will be comprised of greater, fewer or the same number of giant planets as the Solar System, and why? [6 pts] c) The third planet from Nus, Htrae, has a single large moon, Noom. Astronomers learn that the Noom has a low density, has plenty of volatiles and that Htrae is spinning extremely rapidly. Based on this information, what is the most favorable hypothesis explaining the origin of Noom?

I would say that the system will be comprised of the same number as the solar system due to the fact the gas giants would be beyond the frostline where the suns heat would start to diminish, kind of like in our solar system. The heavier elements like rock and metal will stay inside the frost line and that might even lead to more terrestrial-like planets in Nus' system, but the lighter elements like hydrogen and helium are captured by the planets with enough mass to do so outside of the frostline.
Anyone want to correct me?
Noom has a lower density because the impact of giant protoplanetary collision gouged out the outer crust and mantle, and didn’t eject so much of the Htrae's iron core.The huge cloud of ejected debris coalesced into the Noom. The object that collided with Htrae mustve been huge and abundant in volatiles, hence the traces in its composition.
Is it safe to say the fast spinning of Htrae has to do with the the size of the object that collided with it?

Start a new thread, please.