The CMBR is widely accepted as evidence for the Big Bang theory because it represents the afterglow of the early Universe. Shortly after the Big Bang, the Universe was extremely hot and dense. This initial period was a plasma of particles and photons, constantly interacting. As the Universe expanded, it cooled.

Approximately 380,000 years after the Big Bang, the Universe had cooled sufficiently for electrons and protons to combine and form neutral hydrogen atoms. This event is known as recombination. Before recombination, photons were constantly scattered by free electrons, preventing them from travelling freely. However, after recombination, photons could travel unimpeded. This "first light" released during recombination has been travelling through the expanding Universe ever since.

As the Universe expanded, the wavelengths of these photons were stretched, resulting in a decrease in energy and a shift towards longer wavelengths. This stretching has cooled the radiation to the microwave region of the electromagnetic spectrum. The CMBR is observed today as a faint, nearly uniform microwave radiation coming from all directions in space.

The observed properties of the CMBR – its blackbody spectrum with a temperature of approximately 2.7 Kelvin – are precisely what the Big Bang theory predicts. The redshift observed in the CMBR is consistent with the expansion of the Universe. Therefore, the CMBR provides strong evidence that the Universe originated from a hot, dense state and has been expanding ever since.

The CMBR was produced during a period in the early Universe called recombination, which occurred approximately 380,000 years after the Big Bang. Initially, the Universe was a very hot, dense plasma of protons, neutrons, and electrons. Photons were constantly interacting with these charged particles, preventing them from travelling freely.

As the Universe expanded and cooled, the temperature eventually dropped to a point where electrons and protons could combine to form neutral hydrogen atoms. This process is recombination. With fewer free electrons to scatter them, photons were able to travel freely through space. This "first light" released during recombination is what we observe today as the CMBR.

The expansion of the Universe has significantly affected the wavelength and energy of the CMBR. As the Universe expanded, the wavelengths of the photons have been stretched. This phenomenon is known as cosmological redshift. The greater the expansion, the greater the redshift.

This stretching of the wavelength corresponds to a decrease in energy. The photons that were initially very high-energy have been cooled to the microwave region of the electromagnetic spectrum. The current temperature of the CMBR is approximately 2.7 Kelvin, which is a direct result of this expansion and redshift. The observed spectrum of the CMBR is a nearly perfect blackbody spectrum, consistent with the prediction of a uniformly expanding Universe.

Given:

• Redshift (z) = 0.05
• Speed of light (c) = 3.0 x 10⁸ m/s

Formula:

v = zc

Calculation:

v = 0.05 x (3.0 x 10⁸ m/s) = 1.5 x 10⁷ m/s

Answer: The galaxy is moving away from the Earth at a speed of 1.5 x 10⁷ m/s.

Assumptions:

• The redshift is due to the Doppler effect caused by the galaxy's motion away from the Earth.
• The speed of light is constant.
• The galaxy is moving in a straight line relative to the Earth.