Question

For a specific wavelength 670 nm of light from a galaxy moving with velocity ν, the observed wavelength is 670.7 nm. The value of ν is

• A. 3 × 10⁸ ms^–1
• B. 3 × 10¹⁰ ms^–1
• C. 3.13 × 10⁵ ms^–1
• D. 4.48 × 10⁵ ms^–1

Answer 1

The Correct Option is C

The correct answer is (C) : 3.13 × 10⁵ ms^–1

λ_obs = λ_source \(\sqrt{\frac{1+\frac{ν}{C}}{1-\frac{v}{C}}}\)
For ν << C,
\(\frac{670.7}{670}\) = 1 + \(\frac{ν}{C}\)
⇒ ν = \(\frac{0.7}{670}\) × 3 × \(10^8\) m/s
⇒ ν ≃ 3.13 × \(10^5\) m/s