Question

A galaxy moves with respect to us so that sodium light of 589.0 nm is observed at 589.6 nm. The speed of the galaxy is:

• A. $206kms^{- 1}$
• B. $306kms^{- 1}$
• C. $103kms^{- 1}$
• D. $51kms^{- 1}$

Answer 1

Answer: (B)

$306kms^{- 1}$

Answer 2

: the relation between $\upsilon,c$and $\lambda$ are $\upsilon\lambda = c$

For small changes in $\upsilon$and $\lambda$

$\frac{\Delta\upsilon}{\upsilon} = \frac{- \Delta\lambda}{\lambda}$

As $\Delta\lambda = 589.6 - 589.0 = + 0.6nm$

There fore , using Doppler shift

$\frac{\Delta\upsilon}{\upsilon} = \frac{- \Delta\lambda}{\lambda} = \frac{- v_{radial}}{c}$

Or $v_{radial} \cong + c\left( \frac{0.6}{589.0} \right) = + 3.06 \times 10^{5}ms^{- 1} = 306kms^{- 1}$

Therefore , the galaxy is moving away from us