In the laboratory, a spectral line of an element has a wavelength of 5000 Angstroms. What would be the measured wavelength of that line in the spectrum of a planet which is approaching at a velocity of 30 km/s? (The speed of light is 300,000 km/s.)

Respuesta :

Answer:

The wavelength of that line in the spectrum of a planet is [tex]5000.5\ \AA[/tex].

Explanation:

Given that,

Wavelength [tex]\lambda= 5000\ \AA[/tex]

Velocity = 30 km/s

We need to calculate the wavelength of that line in the spectrum of a planet

Using formula of wavelength

[tex]\lambda=\lambda'\sqrt{\dfrac{1-\dfrac{v}{c}}{1+\dfrac{v}{c}}}[/tex]

Where, v = velocity of planet

c = speed of light

Put the value into the formula

[tex]5000=\lambda'\sqrt{\dfrac{1-\dfrac{30\times10^{3}}{3\times10^{8}}}{1+\dfrac{30\times10^{3}}{3\times10^{8}}}}[/tex]

[tex]\lambda'=\dfrac{5000\times10^{-10}}{\sqrt{\dfrac{1-\dfrac{30\times10^{3}}{3\times10^{8}}}{1+\dfrac{30\times10^{3}}{3\times10^{8}}}}}[/tex]

[tex]\lambda'=5000.5\ \AA[/tex]

Hence, The wavelength of that line in the spectrum of a planet is [tex]5000.5\ \AA[/tex].