   Chapter 30, Problem 55PE

Chapter
Section
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= to nf=1 )

Formula Used:

The wavelength and energy is related as follows:

λ=hcΔE

Where λ= Wavelength

h= Planck's Constant

c= speed of light

ΔE= energy change for the transition

Observed wavelength is calculated as

λObserved=λ1+uc1uc

Where, u= Velocity of object

c= Speed of light

Calculation:

Energy change is calculated as

ΔE=EfEi

ΔE=(Z2nf2Eo)(Z2ni2Eo)

We have, Eo=13.6eV , ni= and nf=1

Substituting the values, we have

ΔE=(122Eo)(1212Eo)

ΔE=0(1212(13.6eV))

ΔE=13.6eV

Thus, wavelength is calculated as

λ=hcΔE

λ=1.24×103eV.nm13

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