SATHEE: Waves - Result Question 79

Waves - Result Question 79

81. A star, which is emitting radiation at a wavelength of $5000 \AA$ , is approaching the earth with a velocity of $1.50 \times 10^{6} m / s$ . The change in wavelength of the radiation as received on the earth is

(a) $0.25 \AA$

(b) $2.5 \AA$

(d) $250 \AA$

[1996]

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Answer:

Correct Answer: 81. (c)

Solution:

We know that wavelength of the approaching $s t a r (λ^{'}) = λ (\frac{c - v}{c})$

or, $\frac{λ^{'}}{λ} = \frac{c - v}{c} = 1 - \frac{v}{c}$

or, $\frac{v}{c} = 1 - \frac{λ^{'}}{λ} = \frac{λ - λ^{'}}{λ} = \frac{Δ λ}{λ}$

Therefore, $Δ λ = λ \times \frac{v}{c} = 5000 \times \frac{1.5 \times 10^{6}}{3 \times 10^{8}} = 25 \AA$ [where $Δ λ =$ Change in the wavelength]

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Waves - Result Question 79

81. A star, which is emitting radiation at a wavelength of 5000\AA, is approaching the earth with a velocity of 1.50×106m/s. The change in wavelength of the radiation as received on the earth is

Answer:

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81. A star, which is emitting radiation at a wavelength of $5000 \AA$ , is approaching the earth with a velocity of $1.50 \times 10^{6} m / s$ . The change in wavelength of the radiation as received on the earth is