Cosmic microwave background radiation - Question 100S: Short Answer
The Universe as a perfect (black-body) radiator at 2.7 K
This question is about the temperature of the Universe and the radiation that has filled it since neutral atoms were first produced.
Plasma absorbs photons
It is thought that the early Universe was too hot for electrons and protons to combine together to form neutral atoms, but they existed as a mixture of positive ions and electrons (a plasma). In these conditions photons cannot travel freely, as electromagnetic photons continually interact with the ions, so dense plasma is not transparent.

1.	'Hot atoms' are atoms with large quantities of random kinetic energy. Explain why such atoms would break down into electrons and positive ions.

2.	The radiative zone of a star like our Sun consists of dense plasma. Explain why the photons generated in the Sun’s core take millions of years to travel across the radiative zone.

The photons generated in the core are gamma photons of frequency » 4 × 1017 Hz. The radiative zone gets cooler and cooler from the core to the convective zone. By continual absorption and emission in the radiative zone, photons of lower energy are produced. Eventually, the photon energy is transferred by convection to the photosphere (the Sun’s surface), where photons of frequency » 6 × 1014 Hz are emitted.

3.	Show that, for each gamma photon produced in the core, about 600 photons are emitted from the Sun’s surface.

The Universe becomes transparent
Electromagnetic radiation could not travel through the early Universe, filled with charged particles like the radiative zone of a star. As the Universe expanded, it cooled.
About 105 years after the Big Bang, the Universe had cooled to 3000 K, when the ions in the plasma combined to form stable neutral atoms. The photons produced in the combination were now free, in the absence of the plasma, to travel throughout the Universe.

Wilhelm Wien investigated the radiation emitted by a ‘black-body’ (a perfect emitter) at a temperature T (in kelvin) and deduced that the peak of the distribution of energies it emits occurs at a wavelength l given by 
lT = 2.9 × 10–3 m K

This is Wien’s displacement law, for which he received the Nobel Prize in 1911. You can apply this to the entire Universe, which acts as a perfect emitter, giving out the radiation with which it fills itself.

4.	Use Wien’s law to find the peak wavelength emitted by the Universe at 3000 K.

5.	In what region of the electromagnetic spectrum would you expect to detect this radiation?

6.	3000 K is about the temperature of the tungsten wire in a light bulb. Why do tungsten light bulbs produce so much heat? Why does the glass envelope get so hot?

The Universe expands to its current size
As the Universe has expanded, the photons that fill it have been stretched in wavelength.
7.	Theory suggests that the Universe has now cooled to a temperature of 2.7 K. Use Wien’s law to find the peak wavelength emitted by the Universe at 2.7 K. Why is this radiation referred to as cosmic microwave background radiation?

8.	Show that the diameter of the Universe is currently about 1000 times larger than it was when it became transparent.

9.	Arno Penzias and Robert Wilson first detected the cosmic microwave background radiation from an observatory on Earth's surface. Suggest reasons why accurate measurements of this radiation, which confirm the temperature of the Universe as 2.735 K, needed to be done from a satellite.