You observe a spectral line of hydrogen at a wavelength of 522.5 nm in a distant galaxy. The rest wavelength of this line (known as Hβ or hydrogen beta) is 486.1 nm. What is the radial velocity of this galaxy in kilometers per second? Is it moving toward or away from Earth?

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Answer:

Solved

Explanation:

due to Doppler effect on light

[tex]v= (1-\frac{\lambda}{\lambda_0})c[/tex]

v- radiation velocity of approach

c= velocity of light

λ=522.5 nm  wavelength from the distant star

λ_0 = 486.1 rest wavelength

putting these values to find v

[tex]v= (1-\frac{522.5}{486.1})c[/tex]

=0.0748817*3*10^8

=1.92×10^8 m/ses

=1.92×10^5 Km/sec

since the sign of velocity is negative it is moving away from the Earth.

The radial velocity will be "[tex]1.92\times 10^5[/tex] km/sec".

Doppler effect:

It defines the frequency variations of any type of sound or light wave produced by a moving source throughout the relation to something like an observer.

Waves released by such an item moving towards another observer are compressed, resulting in a greater frequency as even the source gets closer towards the viewer.

According to the question,

Wavelength from distant star,

[tex]\lambda = 522.5[/tex] nm

Rest wavelength,

[tex]\lambda_0 = 486.1[/tex] nm

Velocity of light,

c = [tex]3\times 10^8[/tex]

By using the Doppler effect,

→ v = [tex](1- \frac{\lambda}{\lambda_0} )c[/tex]

By substituting the values,

     = [tex](1-\frac{522.5}{486.1} )\times 3\times 10^8[/tex]

     = [tex]0.0748817\times 3\times 10^8[/tex]

     = [tex]1.92\times 10^8[/tex] m/s

or,

     = [tex]1.92\times 10^5[/tex] km/s

Thus the above answer is right.

Find out more information about Doppler effect here:

https://brainly.com/question/4052291