   Chapter 30, Problem 71PE

Chapter
Section
Textbook Problem

Construct Your Own ProblemConsider the Doppler-shifted hydrogen spectrum received from a rapidly receding galaxy. Construct a problem in which you calculate the energies of selected spectral lines in the Balmer series and examine whether they can be described with a formula like that in the equation 1 λ = R ( 1 n f 2 − 1 n i 2 ) , but with a different constant R.

To determine

Consider the Doppler-shifted hydrogen spectrum received from a rapidly receding galaxy. Construct a problem in which you calculate the energies of selected spectral lines in the Balmer series and examine whether they can be described with the formula like that in the equation1λ=R(1nf21ni2) but with a different constant R.

Explanation

Given Data:

Given that the Doppler-shifted hydrogen spectrum received from a rapidly receding galaxy.

Formula Used:

The observed wavelength in Doppler effect is calculated as

λo=λs1+vc1vc

Whereλs= Wavelength emitted by source

v= Speed of galaxy

c= Speed of light

Wavelength can be calculated as follows

1λ=R(1nf21ni2)

WhereR= Rydberg Constant

nf= Final energy state of electron

ni= Initial energy state of electron

Calculation:

Let us assume a galaxy receding with a speed of0.9c from the Milky way galaxy.

Also assume that the Doppler shifter wavelength isHα

We knowλs=656.4nm andv=0.9c

Thus, observed wavelength is calculated as

λo=(656.4nm)1+0.9cc10

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