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

Answer:

$\lambda_x=5.019858nm$

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

$\lambda=\lambda _0 *\frac{v}{c}$

where

$\lambda_0= length\ of\ spectral\ line$

$c=The\ speed\ of\ light$

$v= speed\ of\ moving\ object$

therefore

$\lambda=5.02*10^{-9} *\frac{8.46*10^{12}}{299 792 458*10^9}$

$\lambda=1.42*10^{-4} nm$

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

$\lambda_x=5.019858nm$