Special Relativity - Doppler Effect

The Lyman alpha spectral line of Hydrogen (λ = 122 nanometers) differs by 1.8 × 10−12 meter in spectra taken at opposite ends of the Sun’s equator. What is the speed of a particle on the equator due to the Sun’s rotation, in kilometers per second?

A. 0.22
B. 2.2
C. 22
D. 220
E. 2200
(GR9677 #60)
Solution:

The problem deals with v ≪ c since the  answer is in km/s.

For v ≪ c, Redshift parameter, z = Δλ/λ v/c

=  cΔλ/λ

Given:
Δλ 1.8 × 10−12 m 
λ 122 nm = 1.22 × 10−7 m
c × 108 m/s


= (× 108)(1.8 × 10−12)/(1.22 × 10−7) 
= (5.4/1.22) × 10m/s  
= (5.4/1.22) km/s ≈ 2.2 km/s

Answer: B

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