Question

Galaxies that are 400 million light years away have a red shift of 0.03 approximately. A radio wave coming from one of these galaxies has an observed wavelength of 125 meters. What is the emitted wavelength in meters and the observed frequency in Megahertz

Answer 1

The correct answer is "121.36 meters and 2.40 MHz".

Step-by-step explanation:

Given:

Red shift,

`(v)/(c)=(\lambda - \lambda_0)/(\lambda_0) = 0.03`

Wavelength,

`\lambda = 125 \ meters`

The observed frequency will be:

⇒
`f = (c)/(\lambda)`

`=(3* 10^8)/(125)`

`=24* 10^5`

`= 2.40* 10^6`

`=2.40 \ MHz`

hence,

The Emitted wavelength will be:

⇒
`(125-\lambda_0)/(\lambda_0) =0.03`

`(125)/(\lambda_0)-1 =0.03`

`125=1.03 \ \lambda_0`

`\lambda_0=(125)/(1.03)`

`=121.36 \ m`