Question

If a galaxy moving away from the Earth has a speed of 1000 km/s and emits 656 nm light characteristic of hydrogen (the most common element in the universe).

What wavelength would we observe on the Earth?
a) 659 nm
b) 656 nm
c) 652 nm
d) 660 nm

Answer 1

Using the Doppler effect, we calculate the wavelength observed on Earth for light emitted from a galaxy moving away at 1000 km/s to be approximately 658 nm, which is redshifted from the original 656 nm. This is considered visible light in the red spectrum, and the Earth's orbital speed is negligible compared to the speed of light and the galaxy's relative velocity.

Step-by-step explanation:

To determine the observed wavelength of light from a galaxy moving away from us, we use the Doppler effect for electromagnetic waves, which states that if a source is moving away, the observed wavelength will be redshifted (longer). The formula for calculating the observed wavelength
`(\( \lambda_(obs) \))` is:

`\( \lambda_(obs) = \lambda_(emit) + (v)/(c) * \lambda_(emit) \),`where:

`\( \lambda_(emit) \)` is the emitted wavelength (656 nm in this case),

• 
  `\( v \)`is the speed of the galaxy relative to Earth (1000 km/s), and
• 
  `\( c \)` is the speed of light in vacuum (approximately 300,000 km/s).

Plugging the values in, we get the observed wavelength as:

`\( \lambda_(obs) = 656 \text{ nm} + \left(\frac{1000 \text{ km/s}}{300,000 \text{ km/s}}\right) * 656 \text{ nm} \)`

`\( \lambda_(obs) = 656 \text{ nm} + (1)/(300) * 656 \text{ nm} \)`

`\( \lambda_(obs) = 656 \text{ nm} + 2.18666667 \text{ nm} \approx 658 nm \)`

The type of electromagnetic radiation in question is visible light, specifically in the red part of the spectrum. The speed of the Earth in its orbit is negligible in this context because it is much smaller than the speed of light and the relative speed of the galaxy.