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?

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

answer: electrons