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Suppose that you'd like to find out if a distant star is moving relative to the earth. The star is much too far away to detect any change in its brightness as it moves toward or away from the earth. Instead we can use the Doppler effect to determine its relative speed. For this problem we are going to look at the spectral lines from hydrogen, specifically the one with a wavelength of 656.46 nm.

Required:
What is V(star) , the speed at which the star is moving relative to the earth?

Respuesta :

Cricetus

Answer:

The speed will be "18km/s". A further explanation is given below.

Explanation:

According to the question, the values are:

Wavelength,

[tex]\lambda = 656.46 \ nm[/tex]

[tex]\Delta \lambda = 0.04[/tex]

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

As we know,

⇒  [tex]\frac{\Delta \lambda}{\lambda} =\frac{v}{c}[/tex]

On substituting the values, we get

⇒  [tex]\frac{656.46}{0.04} =\frac{v}{3\times 10^8}[/tex]

⇒         [tex]v=\frac{656.46}{0.04} (3\times 10^8)[/tex]

⇒            [tex]=16411.5\times 3\times 10^8[/tex]

⇒            [tex]=18280 \ m/s[/tex]

or,

⇒            [tex]=18 \ km/s[/tex]

The  speed at which the star is moving relative to the earth is 18 km/s

Calculation of the speed:

Since the wavelength is  656.46 nm.

And, Δλ=0.04nm

Here Wavelength should represent the distance between the same points in the cycles of a signal propagated in space or it should be along a wire.

Now the speed should be

[tex]= 0.04 \div 656.46 \times 3 \times 10^8[/tex]

= 1820m/s

= 18 km.s

Therefore, The  speed at which the star is moving relative to the earth is 18 km/s

learn more about speed here: https://brainly.com/question/24692367

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