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Hydrogen has a prominent emission line at 486 nm. It was measured for a moving astronomical object at 484 nm. Is the object moving towards or away from the observer and how fast?

A) Moving towards at 2 nm/s
B) Moving away at 2 nm/s
C) Moving towards at 1 nm/s
D) Moving away at 1 nm/s

User Mkab
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1 Answer

4 votes

Final answer:

The astronomical object with a measured emission line at 484 nm, originally at 486 nm, is moving towards the observer. The speed calculated using the Doppler Effect formula is approximately 1233 km/s.

Step-by-step explanation:

The phenomenon in question is the Doppler Effect in astrophysics attributed to the spectral lines of hydrogen. The observed wavelength being shorter than the emitted wavelength (486 nm observed versus 484 nm emitted) indicates that the astronomical object is moving towards the observer. To calculate the speed, we use the formula for relativistic Doppler shift:

v = c * ((λ_observed - λ_emission) / λ_emission)

Where λ_observed is the observed wavelength, λ_emission is the emission wavelength, c is the speed of light (approximately 3 × 108 m/s), and v is the velocity of the object relative to the observer.

Plugging the given wavelengths into the formula:

v = 3 × 108 m/s × ((484 nm - 486 nm) / 486 nm)

v = -1.233 × 106 m/s or approximately -1233 km/s

The negative sign indicates that the object is moving towards us, so the correct answer is that the object is moving towards the observer, and the speed is around 1233 km/s, not 1 nm/s or 2 nm/s as suggested in the options provided.

User Creaktive
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