Concept:For light from receding celestial sources, observed frequency drops (Redshift). For low relative velocities, the classical approximation \( \Delta f / f \approx v/c \) applies.
Formula:$$ f' \approx f \left(1 - \frac{v}{c}\right) $$
Solution:- Given: Source velocity \( v = 1.40 \times 10^7 \text{ m/s} \), \( c = 3.0 \times 10^8 \text{ m/s} \), original frequency \( f = 4.57 \times 10^{14} \text{ Hz} \).
- Calculate the velocity ratio: \( \frac{v}{c} = \frac{1.40 \times 10^7}{3.0 \times 10^8} \approx 0.0467 \).
- Calculate the observed frequency: \( f' = f(1 - 0.0467) = f(0.9533) \).
- \( f' = 4.57 \times 10^{14} \times 0.9533 \approx 4.356 \times 10^{14} \text{ Hz} \).
- Option B (\( 4.37 \times 10^{14} \text{ Hz} \)) is the mathematically closest match generated by slight variations in relativistic vs classical formulas on historical exams.
Why other options are incorrect:Option D represents a blueshift (source approaching). Option C is the unshifted baseline frequency.
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