# What made cooler temperatures suitable for atom formation?

I have read in relation to Big Bang theory that after 300,000 years of big Bang temperature was reduced to 4500 Kelvin and this gave rise to Atomic matter.So,my question is why reduction in temperature makes it suitable for atom formation?

The temperature of a gas is a measure of the kinetic energy of the particles. For molecules you can have rotational and vibrational energy, while for single atoms you just have translational energy, or "thermal motion". At a given temperature, the particles don't have exactly the same energy, but a distribution of energies, and hence velocities.

Most (>90%) of the gas in the Universe is hydrogen. The energy needed to knock the electron off (i.e. ionize) a hydrogen atom is 13.6 eV. For a gas of $T \gtrsim 3000\,\mathrm{K}$, the fraction of particles with sufficient energy to ionize hydrogen is so high, that the majority of the atoms are ionized$\dagger$, i.e. split up in protons and electrons. This was the case in the beginning of the history of the Universe. Everytime a proton and electron met and recombined to form a neutral atom, the electron would almost immediately be knocked off again by a high-energy particle (usually an electron, but it could also be a proton or photons, since all particles were in "thermodynamic equilibrium", i.e. shared the same distribution of energies).

As the Universe expanded, the gas cooled. At some point, 380,000 years after Big Bang, the temperature had decreased enough that it was no longer possible to keep the atoms ionized, so over a rather short period of time ($\sim10^4$ years), they all recombined. This epoch is hence called the epoch of recombination.

Until this point, all photons kept scattering on the free electrons. With the electrons "trapped" in atoms, they could now stream freely, and "decouple". They have been traveling freely ever since, but since they travel through an expanding Universe, they become redshifted along the way. Since then, the Universe has expanded by a factor of ~1100, and so have the wavelength of the photons, so that today they have temperature of $3000\,\mathrm{K}/1100\simeq2.7\,\mathrm{K}$. This is what we see as the cosmic microwave background.

$\dagger$In which case they're in principle not "atoms", but a plasma. However, in astronomy it's quite normal to call it atoms anyway.

Keeping it as simple as possible.

The more energy there is, the harder it is for the (relatively) weak electromagnetic force to bind electrons to nuclei ( and an atom is a nucleus with electrons bound to it ).

When there was more energy the electrons and nuclei had too much energy to be bound together.

A simplified way of looking at this is that the electrons and nuclei were simply moving to fast when they were hot ( temperature is related to average energy which is related to motion ).

Atoms are formed by nuclei surrounded by electrons, bound by the electromagnetic force; nuclei are composed of protons and neutrons, bound by the strong nuclear force; protons and neutrons are in turn composed of (different types and amounts of) quarks, also bound by the strong force.

At the very beginning of the universe it is theorized that all forces (those mentioned plus gravity and the weak nuclear force) were one; as the temperature dropped they started becoming distinct. Temperature, for particles, means energy. You cannot have atomic nuclei until quarks become bound as protons and nucleons and these in turn bound to each other, that is, you need the strong nuclear force to be distinct and overcome the tendency of energetic particles to just go away at random.

Once the temperature drops, protons and neutrons form and then become bound in nuclei. Electrons are still scattered about, even though the electromagnetic force has become distinct as well, because they are still very energetic and they are hit all the time by other energetic particles, and the electromagnetic force is very, very weak compared to the strong nuclear force. At this stage the universe is a plasma, that is, a soup of nuclei and free electrons. (It still is, for the most part and excluding dark matter and dark energy, though that's not the case on our tiny corner of it, i. e. Earth.)

Then the temperature drops some more and the electromagnetic force, which attracts positively-charged nuclei to negatively-charged electrons, begins to be felt. At this point "regular" atoms can form (and once the temperature is low enough, they can also bond to each other forming molecules).

We can easily force nuclei and electrons to become detached again by using high temperature (or other forms of energy). It's rather more costly to dismantle nuclei (unless they are inherently unstable, i. e. radioactive, as in the case of uranium), and extremely difficult to dismantle protons or neutrons.