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

1. 0.25 Å
2. 2.5 Å
3. 25 Å
4. 250 Å

Correct answer: 2.5 Å

Solution

The Doppler effect for light gives the change in wavelength as Δλ = (v/c)λ, where v is the velocity of the source, c is the speed of light, and λ is the original wavelength. Substituting v = 1.50 × 10⁶ m/s, c = 3 × 10⁸ m/s, and λ = 5000 Å = 5 × 10⁻⁷ m, we get Δλ = (1.50 × 10⁶ / 3 × 10⁸) × 5 × 10⁻⁷ = 2.5 × 10⁻¹⁰ m = 2.5 Å.

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