Question

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

• A. 30 days
• B. 24 hours
• C. 25 days
• D. 365 days

Answer 1

Answer: (C)

By Doppler's effect, we have
$\frac{\Delta \lambda}{\lambda}=\frac{v}{c} $
$\Rightarrow \Delta \lambda=\frac{\lambda \Delta}{c}$
Change in wavelength for two edges $=\pm \Delta \lambda$
$\Rightarrow $ Total change is $\delta \lambda=2 \Delta \lambda=2 \frac{\lambda v}{c}$
$\Rightarrow v=\frac{c \delta \lambda}{2 \lambda}$
Time period of revolution is given as
$T=\frac{2 \pi R}{v}=2 \pi R x \frac{2 \lambda}{c \delta \lambda}=\frac{4 \pi R \lambda}{c \delta \lambda} $
$\Rightarrow T=\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
$\Rightarrow T=24.8$ days $ \approx 25 $ days