   Chapter 30, Problem 54PE

Chapter
Section
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

1λ=R(1nf21ni2)

Where λ= Wavelength

R= Rydberg Constant

nf= final energy state of electron

ni= initial energy state of electron

Observed wavelength is calculated as

λObserved=λ1+uc1uc

Where, u= Speed of Earth

c= Speed of light

Calculation:

Wavelength is calculated as

1λ=R(1nf21ni2)

We have R=1.097×107m1

ni=7

nf=2

Substituting the above values, wavelength is calculated as

1λ=(1.097×107m1)(122172)

1λ=(1

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