Chapter 30, Problem 54PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# Integrated ConceptsA galaxy moving away from the earth has a speed of 0.0100c. What wavelength do we observe for an n i = 7 to n f = 2 transition for hydrogen in that galaxy?

To determine

The wavelength we observe for an ni=7 to nf=2 transition for hydrogen in that galaxy.

Explanation

Given Data:

Given that a galaxy moving away from the Earth has a speed of 0.0100c . One observe transition for hydrogen in that galaxy from ni=7 to nf=2

Formula Used:

Wavelength of spectrum lines is given as

â€ƒâ€ƒ1Î»=R(1nf2âˆ’1ni2)

Where Î»= Wavelength

â€ƒâ€ƒR= Rydberg Constant

â€ƒâ€ƒnf= final energy state of electron

â€ƒâ€ƒni= initial energy state of electron

Observed wavelength is calculated as

â€ƒâ€ƒÎ»Observed=Î»1+uc1âˆ’uc

Where, u= Speed of Earth

â€ƒâ€ƒc= Speed of light

Calculation:

Wavelength is calculated as

â€ƒâ€ƒ1Î»=R(1nf2âˆ’1ni2)

We have R=1.097Ã—107mâˆ’1

â€ƒâ€ƒni=7

â€ƒâ€ƒnf=2

Substituting the above values, wavelength is calculated as

â€ƒâ€ƒ1Î»=(1.097Ã—107mâˆ’1)(122âˆ’172)

â€ƒâ€ƒ1Î»=(1

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