A spectral line of wavelength 0.59 mm is observed in the directions to the opposite edges of the solar disc along its equator. A difference in wavelength equal to $(Δλ)$ 8 picometer is observed. Period of Sun's revolution around its own axis will be about (Radius of sun = $6.95 × 10^8 m$)
Answer & explanation
Correct answer: option 3
$\frac{Δλ}{λ}=\frac{v}{c}$ or $Δλ=\frac{λΔ}{c}$
Change in wavelength for two edges = $±Δλ$
Total change, $δλ=2Δλ$
$=2\frac{λv}{c}$ or $v=\frac{c\,δλ}{λ}$
and $T=\frac{2πR}{v}=2πR×\frac{2λ}{c\,δλ}=\frac{4πRλ}{c\,δλ}$
$=\frac{4×3.14×6.95×10^8×0.59×10^{-6}}{3×10^8×8×10^{-12}×86400}$days
24.8 days ≈ 25 days