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A galaxy recedes from the Earth at a speed of 286 km/s. A spectral red line, normally at 630 nm, is observed to shift in wavelength by an amount x x 10⁻¹⁰ m. Find x to the nearest integer. (Take c = 3 x 10⁸ m/s.)

1. x = 6
2. x = 3
3. x = 12
4. x = 9

Correct answer: x = 6

Solution

For a receding source the wavelength shift is delta(lambda) = lambda*(v/c). Here lambda = 630e-9 m, v = 286e3 m/s, c = 3e8 m/s. delta(lambda) = 630e-9*(286e3/3e8) = 630e-9*(9.533e-4) = 6.0e-10 m. So x = 6.

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