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  • A spectral line of wavelength  is observed in the directions to the opposite e

A spectral line of wavelength 0.59 \mathrm{~mm}  is observed in the directions to the opposite edges of the solar disc along its equator. A difference in wavelength equal to (\Delta \lambda) 8 picometer is observed. Period of Sun's revolution around its own axis will be about (Radius of sun =6.95 \times 10^{8} \mathrm{~m} )

Option: 1

30 days


Option: 2

 24 hours


Option: 3

25 days


Option: 4

365 days


Answers (1)

best_answer

\mathrm{\frac{\Delta \lambda}{\lambda}=\frac{v}{\mathrm{c}} \text { or } \Delta \lambda=\frac{\lambda \Delta}{\mathrm{c}}}
Change in wavelength for two edges \mathrm{= \pm \Delta \lambda}

Total change, \mathrm{\delta \lambda=2 \Delta \lambda}
\mathrm{=2 \frac{\lambda v}{c} \text { or } v=\frac{c \delta \lambda}{2 \lambda}}
\mathrm{and \, \mathrm{T}=\frac{2 \pi \mathrm{R}}{\mathrm{v}}=2 \pi \mathrm{R} \times \frac{2 \lambda}{\mathrm{c} \delta \lambda}=\frac{4 \pi \mathrm{R} \lambda}{\mathrm{c} \delta \lambda}}

\mathrm{=\frac{4 \times 3.14 \times 6.95 \times 10^{8} \times 0.59 \times 10^{-6}}{3 \times 10^{8} \times 8 \times 10^{-12} \times 86400}\, days}

\mathrm{24.8 days \approx 25 days}

 

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Sayak

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