   Chapter 28, Problem 30PE

Chapter
Section
Textbook Problem

Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive 1900 nm electromagnetic radiation and know that it was 1875 nm when emitted by the hydrogen gas. What is the speed of the gas?

To determine

The speed of the hydrogen gas.

Explanation

Given info:

• The wavelength of electromagnetic radiation emitter by hydrogen gas is 1875nm .
• The wavelength of radiation received is 1900nm .

Formula used:

Formula to find the wavelength of radiation observer by the observer on Earth

λ0=λs1+uc1uc

Here, λ0 is the wavelength of the emitted radiation observed on Earth, λs wavelength of radiation emitted by the hydrogen gas, u is the velocity of the hydrogen gas and c is the speed of light.

Rearrange the formula to find the speed of the hydrogen gas,

( λ 0 λ s )2=1+uc1ucλ02(1uc)=λs2(1+uc)u=

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