Question

If the peak wavelength of a star at rest is 830 nm, but astronomers on earth observer that is has been shifted by 3.2 nm. Then how fast is the star moving relative to the earth

Answer 1

The star is moving away from the Earth with a speed of 1.16 x 10⁶ m/s.

Step-by-step explanation:

According to the question, the peak wavelength of the star at rest is 830 nm, but it has been observed to be shifted by 3.2 nm. Since the wavelength has been shifted to a longer wavelength, the star is moving away from the observer.

To determine the speed of the star relative to the Earth, we can use the formula:

Speed = (Change in wavelength / Rest wavelength) * Speed of light

By plugging in the given values, we get:
Speed = (3.2 nm / 830 nm) * 3.0 x 10⁸ m/s = 1.16 x 10⁶ m/s

Answer 2

The speed is
`v  =   1.16 *10^(6) \  m/s`

Step-by-step explanation:

From the question we are told that

The peak wavelength is
`\lambda  = 830 \  nm  =  830  *10^(-9) \ m`

The magnitude of the shift is
`\Delta  \lambda = 3.2 nm  =  3.2*10^(-9) \  m`

Generally the doppler shift equation is mathematically represented as

`(\Delta \lambda)/( \lambda)  =  (v)/(c)`

=>
`v  =  c * [(\Delta  \lambda)/(\lambda) ]`

Here c is the speed of light with value
`=  3.0*10^(8) \  m/ s`

So

=>
`v  =   1.16 *10^(6) \  m/s`