The wavelength of light from a star is 0.4% m | vedclass

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Question

(B) According to the Doppler effect for light,the fractional change in wavelength is given by $\frac{\Delta \lambda}{\lambda} = \frac{v}{c}$,where $v$

Vedclass · Accepted Answer

$1.2 	imes 10^3 \, km/s$

Vedclass · Answer

(B) According to the Doppler effect for light,the fractional change in wavelength is given by $\frac{\Delta \lambda}{\lambda} = \frac{v}{c}$,where $v$ is the relative velocity of the source and $c$ is the speed of light $(3 	imes 10^8 \, m/s)$.Given that the wavelength is $0.4\%$ more,we have $\frac{\Delta \lambda}{\lambda} = 0.4\% = \frac{0.4}{100} = 4 	imes 10^{-3}$.Using the formula $v = \frac{\Delta \lambda}{\lambda} 	imes c$,we get:$v = (4 	imes 10^{-3}) 	imes (3 	imes 10^8 \, m/s) = 12 	imes 10^5 \, m/s = 1.2 	imes 10^6 \, m/s$.Converting to $km/s$ by dividing by $1000$:$v = \frac{1.2 	imes 10^6}{10^3} \, km/s = 1.2 	imes 10^3 \, km/s$.

The wavelength of light from a star is $0.4\%$ more than the corresponding wavelength on the Earth. The velocity of the star with respect to the Earth is:

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