Problem

A space probe speeding towards the nearest star m…

03:14

Problem 24 Hard Difficulty

If a galaxy moving away from the Earth has a speed of 1000 $\mathrm{km} / \mathrm{s}$ and emits 656 $\mathrm{nm}$ light characteristic of hydrogen (the most common element in the universe). (a) What wavelength would we observe on the Earth? (b) What type of electromagnetic radiation is this? (c) Why is the speed of the Earth in its orbit negligible here?

Answer

(a) $\lambda=660 \mathrm{nm}$
(b) Visible region and red in color.
(c) It is very small.

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Physics 103

College Physics for AP® Courses

Chapter 28

Special Relativity

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Video Transcript

the speed of the galaxy. Moving away from the earth is 1000 kilometer per second. Is it called too? One pausing kilometer. Uh, her second. Let's gonna work this into meter per second. So 1000 kilometer per second is equal to 1000 multiply by. Killer killing is 10 to the power of three meter for a second and the reverend off the committed light land or not, the prevalent off the emitted light is equal to 656 nanometers. And 656 millimeters uh equals 656 multiplied by 10 to the bowler minus mine meters. And we know that the speed of light is 3.0 Don't multiply by 10 to the Power Age Meet her Her second. Well, the Web land off the light when we observed from the earth is given by lander is equal to lend a knot times squared route off one plus you divided by sea divided by one minus you divided by sea and we have values. Well, uh, let's substitute the values Now Lender is equal to, uh, Lambda Noughties. 600 56 multiplied by tend to the bollard minus line. Multiply by square root huh? One plus 1000. Multiply by 10 to the power of three meter per second. Divided by ah, speed of light and speed of light is three buying 200 multiplied by 10 to the power eight meters per second, divided by one minus 1000 multiplied by 10 to the power tree divided by 3.0 multiplied by 10 to the power eight and therefore Landa is equal to 660. Multiply by 10 to the bollard minus nine meters and since tend to the bar minus nine is mental. Therefore, Lambda is equal to 67 60 nanometers. So Philander is 660 mana meters. Well, let's hope part B well from electromagnetic spectrum um development Lambda is equal to 660 nanometers. Lies in the visible region. Lies and uh visible region visible visible region and the Ventolin land or not, which is equal to 656 nanometers, also lies in the visible region. Uh, also lies in the Wiz Herbal region, Invincible Region and the violent is red in color. Let's do you see Well, the speed of our galaxy is very large, and velocity of the earth is very small, so we can neglect the speed, the speed of the earth. So, a speed. Oh, our galaxy. Ah, speed off our galaxy, uh, is very large eyes very, very greater than the speed of fear. Spiegel are so we can neglect the speed off here. So there speed off the earth. Speed off the earth is neglected. Yes, neglected.

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