Chapter 30, Problem 66PE

### 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 pulsar is a rapidly spinning remnant of a supernova. It rotates on its axis, sweeping hydrogen along with it so that hydrogen on one side moves toward us as fast as 50.0 km/s, while that on the other side moves away as fast as 50.0 km/s. This means that the EM radiation we receive will be Doppler shifted over a range of ± 50.0 km/s. What range of wavelengths will we observe for the 91.20-nm line in the Lyman series of hydrogen? (Such line broadening is observed and actually provides part of the evidence for rapid rotation.)

To determine

What range of wavelengths will we observe for the 91.20nm line in the Lyman series of hydrogen?

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=âˆž to nf=1 )

Formula Used:

Observed wavelength is calculated as

â€ƒâ€ƒÎ»Observed=Î»1+uc1âˆ’uc

Where, u= Velocity of object

â€ƒâ€ƒc= Speed of light

Calculation:

When star is moving towards us

Observed wavelength is calculated as

â€ƒâ€ƒÎ»Observed=Î»1+uc1âˆ’uc

We have, Î»=91.20nm , u=50Ã—103m/s and c=2.99Ã—108m/s

â€ƒâ€ƒÎ»Observed=91.20nm1+ 50Ã— 10 3 m/s 2.99Ã— 10 8 m/s1âˆ’ 50Ã— 10 3 m/s 2

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