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One of the wavelengths of light emitted by hydrogen atoms under normal laboratory conditions is at ?0 = 656.3nm in the red portion of the el
Question
One of the wavelengths of light emitted by hydrogen atoms under normal laboratory conditions is at ?0 = 656.3nm in the red portion of the electromagnetic spectrum. In the light emitted from a distant galaxy this same spectral line is observed to be Doppler-shifted to ? = 953.3nm , in the infrared portion of the spectrum.
How fast are the emitting atoms moving relative to the earth?
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Physics
3 years
2021-07-29T01:08:23+00:00
2021-07-29T01:08:23+00:00 1 Answers
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Answer:
1.07 × 10⁸ m/s
Explanation:
Using the relativistic Doppler shift formula which can be expressed as:
here;
= wavelength measured in relative motion with regard to the source at velocity v
observed wavelength from the source’s frame.
Given that:
= 656.3 nm
953.3 nm
We will realize that > ; thus, v < 0 for this to be true.
From the above equation, let’s make (v/c) the subject of the formula: we have:
v = 0.357 c
To m/s:
1c = 299792458 m/s
∴
0.357c = (299 792 458 × 0.357) m/s
= 107025907.5 m/s
= 1.07 × 10⁸ m/s