Question

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.)

Answer 1

The wavelength of that line in the spectrum of a planet is
`5000.5\ \AA`.

Step-by-step explanation:

Given that,

Wavelength
`\lambda= 5000\ \AA`

Velocity = 30 km/s

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

Using formula of wavelength

`\lambda=\lambda'\sqrt{(1-(v)/(c))/(1+(v)/(c))}`

Where, v = velocity of planet

c = speed of light

Put the value into the formula

`5000=\lambda'\sqrt{(1-(30*10^(3))/(3*10^(8)))/(1+(30*10^(3))/(3*10^(8)))}`

`\lambda'=\frac{5000*10^(-10)}{\sqrt{(1-(30*10^(3))/(3*10^(8)))/(1+(30*10^(3))/(3*10^(8)))}}`

`\lambda'=5000.5\ \AA`

Hence, The wavelength of that line in the spectrum of a planet is
`5000.5\ \AA`.