Question

If astronomers look toward any point in outer space, they see radiation that matches the emission spectrum of an object at 2.7 k, a remnant of the big bang. What is the peak wavelength of this radiation? What part of the electromagnetic spectrum is it in?

Answer 1

The peak wavelength of the cosmic microwave background radiation, which is a remnant of the Big Bang, is approximately 1.06 millimeters, placing it in the microwave region of the electromagnetic spectrum.

Step-by-step explanation:

When astronomers observe the cosmic microwave background radiation (CMBR), they are looking at the most perfect blackbody spectrum known, which is characteristic of a temperature of approximately 2.725 K. This temperature is the cooled remnant of the Big Bang. The peak wavelength of this radiation can be calculated using Wien's Law, which relates the temperature of a blackbody to its peak emission wavelength. Given the temperature of 2.725 K, the peak wavelength (λ_max) can be calculated as:

λ_max = "b" / T

where "b" is Wien's displacement constant (approximately 2.897 x 10^-3 m*K). Plugging in the values, we obtain a peak wavelength of about 1.06 millimeters.

This peak wavelength is within the microwave region of the electromagnetic spectrum. The significance of the CMBR lies in its support for the Big Bang theory, providing evidence of the universe's rapid expansion from a very hot and dense state approximately 10 to 20 billion years ago.