What wavelength would visible light (400 to 700 nm) have if it were seen from a galaxy formed

step 1 This is a question about relativistic Doppler effect. It involves a galaxy which is receding fro

What wavelength would visible light (400 to 700 nm) have...

What wavelength would visible light $(400 \text { to } 700 \mathrm{nm})$ have if it were seen from a galaxy formed just half a billion years after the Big Bang? What if it came from matter when the universe was just $400,000 \text { years old? (Refer to Table } 79.1 .)$

Key Concepts

Scale Factor

The scale factor is a metric used in cosmology to describe how the size of the universe changes over time. It provides a proportional measure of the expansion of space, and differences in the scale factor between epochs directly influence how much wavelengths of light are stretched. By comparing the scale factor at the time of light emission to that at the time of observation, one can determine the extent of redshift, making it essential for understanding the evolving universe.

Recombination Epoch

The recombination epoch refers to the period in the early universe, approximately 400,000 years after the Big Bang, when electrons combined with protons to form neutral hydrogen atoms. This event made the universe transparent to radiation, allowing photons to travel freely. The remnant of these photons observed today as the cosmic microwave background provides a key reference in cosmology for studying the redshift and thermal history of the universe.

Cosmological Redshift

This concept describes the stretching of light's wavelength due to the expansion of the universe. As the universe expands, light traveling through it gets redshifted, meaning its wavelength increases (and its frequency decreases). This is quantified by the redshift parameter (z), where the observed wavelength is (1+z) times the emitted wavelength. This effect is fundamental in observational cosmology for relating the properties of light from distant objects to the expansion history of the universe.

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