Question

A star is receding away from earth with a velocity of ${10}^5{\text{ms}}^{-1}.$ If the wavelength of its spectral line is $5700{\text{A}}^o$ then Doppler shift will be

• A. $0.2{\text{A}}^o$
• B. $1.9{\text{A}}^o$
• C. $20{\text{A}}^o$
• D. $200{\text{A}}^o$

Answer 1

The correct option is B $1.9{\text{A}}^o$

As,we know that Doppler effect in light$,=\frac{△\lambda }{\lambda }=\frac{△f}{f}=\frac{v}{c}$

where, $△\lambda =\text{wavelength shift}$

$△f=\text{frequency shift}$

$v=\text{speed of object}$

$c=\text{speed of light}=3\times {10}^8\text{m/s}$

$\frac{△\lambda }{\lambda }=\frac{v}{c}\Rightarrow △\lambda =\frac{\lambda v}{c}$

$△\lambda =\frac{5700\times {10}^5}{3\times {10}^8}=1.9$