Question

For a specific wavelength $670\, nm$ of light coming from a galaxy moving with velocity $v$, the observed wavelength is $670.7\, nm$. The value of $v$ is :

• A. $3 \times 10^{8}\, ms ^{-1}$
• B. $3 \times 10^{10}\, ms ^{-1}$
• C. $3.13 \times 10^{5} \, ms ^{-1}$
• D. $4.48 \times 10^{5} \, ms ^{-1}$

Answer 1

Answer: (C)

$\lambda_{\text {emitted }}=670 \,nm$
$\lambda_{\text {obs }}=670.7 \,nm$
$v =?$
$c =3 \times 10^{8}\, m / s$
If $v << c$
$\frac{\lambda_{\text {obs }}-\lambda_{\text {emited }}}{\lambda_{\text {emitted }}}=\frac{ v }{ c }$
$\frac{670.7-670}{670}=\frac{ v }{ c }$
$V =3.13 \times 10^{5} \,m / s$