A galaxy is moving away from the earth at a speed of 286 kms ⁻¹. The shift in the wavelength of a redline at 630 nm is x × 10 - 10 m. The value of x, to the nearest integer, is ____________. [Take the value of speed of light c, as 3 × 108 ms ⁻¹ ] Numerical answer type. Work it out, then open the answer.

Answer: 6. Doppler shift: Δλ = /c. Δλ = 630×10⁻⁹ × 286×10³3×10⁸ = 630×10⁻⁹ × 9.53×10⁻⁴ Δλ ≈ 6.0×10⁻¹⁰ m So x = 6.

A galaxy is moving away from the earth at a speed of 286 kms ⁻¹. The… | JEE Main 2021 (18 Mar, Shift 2)

Q17JEE Main 2021 · 18 MAR · SHIFT 2Easy

Wave Theory, Wavefronts & Doppler Effect

A galaxy is moving away from the earth at a speed of 286 kms ${}^{-1}$ . The shift in the wavelength of a redline at 630 nm is x $\times$ 10 $-$ 10 m. The value of x, to the nearest integer, is ____________. [Take the value of speed of light c, as 3 $\times$ 108 ms ${}^{-1}$ ]

Numerical answer type. Work it out, then open the answer.

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Answer: 6

Doppler shift: $\Delta\lambda = \lambda\dfrac{v}{c}$ .
$\Delta\lambda = 630\times10^{-9} \times \dfrac{286\times10^{3}}{3\times10^{8}} = 630\times10^{-9} \times 9.53\times10^{-4}$
$\Delta\lambda \approx 6.0\times10^{-10}$ m
So $x = 6$ .

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Wave Theory, Wavefronts & Doppler Effect question from JEE Main 2021 (18 Mar, Shift 2)

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