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NCERT Class XII Chapter
Wave Optics
Questions With Solutions

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Question : 11 of 21
Marks: +1, -0
The 6563 Å HαH_\alpha line emitted by hydrogen in a star is found to be red shifted by 15 Å. Estimate the speed with which the star is receding from the earth
Solution:  
Here, λ = 6563 Å, Δλ = 15 Å, c = 3 × 108 m s110^8 \text{ m s}^{-1}
Since the star is receding away, hence its velocity v is negative (i.e. if Δλ is positive, v is negative)
∴ Δλ = vλc-\frac{v\lambda}{c} or v = cΔλλ-\frac{c\Delta\lambda}{\lambda} = - 3×108×156563\frac{3 \times 10^8 \times 15}{6563} = - 6.86 × 105ms110^5 \text{ms}^{-1}
Here, negative sign shows recession of star.
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