gen-define-the-cosmic-microwave-background-and-give-one-short-wo-468b

Define the cosmic microwave background and give one short worked example.

# Cosmic Microwave Background (CMB) ## Definition The **Cosmic Microwave Background** is the thermal radiation left over from the early universe, approximately 380,000 years after the Big Bang. At this time, the universe cooled enough (~3000 K) for electrons and protons to combine into neutral hydrogen atoms, allowing photons to travel freely for the first time. These photons have been redshifted by the universe's expansion and now appear as microwave radiation at about **2.7 K**. ## Worked Example: Calculating the Peak Wavelength **Question:** At what wavelength does the CMB radiation peak? **Solution:** Using Wien's Displacement Law: $$\lambda_{max} = \frac{b}{T}$$ where: - b = 2.898 × 10⁻³ m·K (Wien's constant) - T = 2.725 K (CMB temperature) $$\lambda_{max} = \frac{2.898 \times 10^{-3}}{2.725} = 1.06 \times 10^{-3} \text{ m} = 1.06 \text{ mm}$$ **Answer:** The CMB peaks at approximately **1.06 mm**, which is in the microwave region of the electromagnetic spectrum (hence the name).