   Chapter 30, Problem 65PE

Chapter
Section
Textbook Problem

Integrated ConceptsA neighboring galaxy rotates on its axis so that stars on one side move toward us as fast as 200 km/s, while those on the other side move away as fast as 200 km/s. This causes the EM radiation we receive to be Doppler shifted by velocities over the entire range of ± 200 km/s. What range of wavelengths will we observe for the 656.0-nm line in the Balmer series of hydrogen emitted by stars in this galaxy. (This is called line broadening.)

To determine

What range of wavelengths will we observe for the 656nm line in the Balmer series of hydrogen emitted by stars in this galaxy.

Explanation

Given Data:

Given that a star is moving relative to the earth. Also, one observe a wavelength of 91nm for ionized hydrogen capturing an electron directly into the lowest orbital (which is ni= to nf=1 )

Formula Used:

Observed wavelength is calculated as

λObserved=λ1+uc1uc

Where, u= Velocity of object

c= Speed of light

Calculation:

When star is moving towards us

Observed wavelength is calculated as

λObserved=λ1+uc1uc

We have λ=656nm , u=200×103m/s and c=2.99×108m/s

λObserved=656nm1+ 200× 10 3 m/s 2.99× 10 8 m/s1 200× 10 3 m/s 2

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