Chapter 30, Problem 55PE

### 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 ConceptsCalculate the velocity of a star moving relative to the earth if you observe a wavelength of 91.0 nm for ionized hydrogen capturing an electron directly into the lowest orbital (that is, a n i = ∞ to n f = 1 , or a Lyman series transition).

To determine

The velocity of a star moving relative to the earth

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:

The wavelength and energy is related as follows:

â€ƒâ€ƒÎ»=hcÎ”E

Where Î»= Wavelength

â€ƒâ€ƒh= Planck's Constant

â€ƒâ€ƒc= speed of light

â€ƒâ€ƒÎ”E= energy change for the transition

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:

Energy change is calculated as

â€ƒâ€ƒÎ”E=Efâˆ’Ei

â€ƒâ€ƒÎ”E=(âˆ’Z2nf2Eo)âˆ’(âˆ’Z2ni2Eo)

We have, Eo=13.6eV , ni=âˆž and nf=1

Substituting the values, we have

â€ƒâ€ƒÎ”E=(âˆ’12âˆž2Eo)âˆ’(âˆ’1212Eo)

â€ƒâ€ƒÎ”E=0âˆ’(âˆ’1212(13.6eV))

â€ƒâ€ƒÎ”E=13.6eV

Thus, wavelength is calculated as

â€ƒâ€ƒÎ»=hcÎ”E

â€ƒâ€ƒÎ»=1.24Ã—103eV.nm13

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