Question

A star is known to be moving at 8.46km/s toward the earth. If you observe the spectral line to be at 5.02nm, at what wavelength would you expect to measure the spectral line in a lab?

Answer 1

`\lambda_x=5.019858nm`

Step-by-step explanation:

From the question we are told that

Speed of star
`S=8.46km/s`

Distance of spectral line
`\lambda_0= 5.02nm`

Generally the equation for wavelength with respect to spectral lines is mathematically given by

`\lambda=\lambda _0 *(v)/(c)`

where

`\lambda_0= length\ of\ spectral\ line`

`c=The\ speed\ of\ light`

`v= speed\ of\ moving\ object`

therefore

`\lambda=5.02*10^(-9) *(8.46*10^(12))/(299 792 458*10^9)`

`\lambda=1.42*10^(-4) nm`

Generally the equation for new wavelength is mathematically given as

`\lambda_x=\lambda _0-\lambda`

`\lambda_x=5.02 nm-1.42*10^(-4) nm`

`\lambda_x=5.02-1.42*10^(-4)`

Therefore

`\lambda_x=5.019858nm`