Modern Physics-Einstein's Postulates/Relativistic Velocity

[giraffe]

Homework Statement

12. one of the strongest emission lines observed from distant galaxies comes from hydrogen and has a wavelength of 122 nm(in the ultraviolet region).
a) how fast must a galaxy be moving away from us in order for that line to be observed in the visible region at 366 nm?
b) what would be the wavelength of the line if that galaxy were moving toward us at the same speed?

Homework Equations

the book I am using has the chapter separated into smaller sections as you read through it. so it has the problems separated into these same sections so you know what information to look for or need. book is modern physics 3rd edition by kenneth krane

so this question is in the consequences of einstein's postulates. the first one is the principle of relativity and the second one is the principle of the constancy of the speed of light. i do know that this problem would have to do with relativistic velocity addition.

The Attempt at a Solution

i don't know/understand how to develop equations from these two postulates. the book has an example with equations for the relativistic velocity addition but how does wavelength fit into this? this leads me to believe that i need to somehow draw a picture and develop specific equations for this problem. if this is the case, how do i go about doing such a thing with such minimal information? i know that i would need to use us(earth) as one observer point(o) and the other galaxy as another(o').

thanks for all your continued help.

 

[td21]

This question is concerned with relativistic doppler effect:
Attached please find the equation.

Homework Statement

12. one of the strongest emission lines observed from distant galaxies comes from hydrogen and has a wavelength of 122 nm(in the ultraviolet region).
a) how fast must a galaxy be moving away from us in order for that line to be observed in the visible region at 366 nm?
b) what would be the wavelength of the line if that galaxy were moving toward us at the same speed?

Homework Equations

the book I am using has the chapter separated into smaller sections as you read through it. so it has the problems separated into these same sections so you know what information to look for or need. book is modern physics 3rd edition by kenneth krane

so this question is in the consequences of einstein's postulates. the first one is the principle of relativity and the second one is the principle of the constancy of the speed of light. i do know that this problem would have to do with relativistic velocity addition.

The Attempt at a Solution

i don't know/understand how to develop equations from these two postulates. the book has an example with equations for the relativistic velocity addition but how does wavelength fit into this? this leads me to believe that i need to somehow draw a picture and develop specific equations for this problem. if this is the case, how do i go about doing such a thing with such minimal information? i know that i would need to use us(earth) as one observer point(o) and the other galaxy as another(o').

thanks for all your continued help.

 

[giraffe]

so letting lambda be the 366 and lambda sub 0(or lambda not) be the 122 and solving the equation for v i get 0.8c.

 

[Quantum Braket]

Well td21... That was a bit useless as a method of helping the student towards an answer. Not only did you simply give the student a formula, but did so without any explanatory text or looking at their proposed solution.

 

[Quantum Braket]

Yeah Giraffe, if you plug n chug that is what you get. *sigh*

 

[giraffe]

Thanks quantum. I'm only 2-3 wks into school so I'm not quite sure of the type of answers I should be getting as my professor just gives a lot of historical information in lecture but no example problems.

 

[td21]

Well td21... That was a bit useless as a method of helping the student towards an answer. Not only did you simply give the student a formula, but did so without any explanatory text or looking at their proposed solution.

I apologize for giving little explanation on the formula given and the term relativistic doppler effect. I will improve on my approach next time by giving more explanations to the students.
I actually hope the student can look into relativistic doppler effect by himself in the library or in the world wide web and ponder over the equation I gave him. I should not give him the equation.
I apologize for doing so and regret it. I will improve on my answering techniques and approaches in the future.