Question

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 \(\times 10^8\) ms\(^{-1}\)]

Hint:

Doppler Redshift means the wavelength increases (\(\Delta \lambda>0\)) as the source moves away.

Answer 1

Correct Answer: 6

Step 1: Use the Doppler effect formula for light (Redshift): \[ \Delta \lambda = \lambda \frac{v}{c} \]
Step 2: Substitute the values. \(\lambda = 630 \text{ nm} = 630 \times 10^{-9} \text{ m}\) \(v = 286 \text{ kms}^{-1} = 2.86 \times 10^5 \text{ ms}^{-1}\) \(c = 3 \times 10^8 \text{ ms}^{-1}\)
Step 3: Calculate \(\Delta \lambda\). \[ \Delta \lambda = 630 \times 10^{-9} \times \frac{2.86 \times 10^5}{3 \times 10^8} \] \[ \Delta \lambda = 210 \times 10^{-9} \times 0.953 \times 10^{-3} \approx 600 \times 10^{-12} \text{ m} = 6 \times 10^{-10} \text{ m} \] Thus, \(x = 6\).