# How much habitable land is there on earth per person?

What is the total area of habitable land on Earth? And how much habitable land does that leave one person? We’ll use the value r = 6400 km as the radius of Earth. According to the corresponding formula for spheres, the surface area of Earth is:

S = 4 * π * (6400 km)^2 ≈ 515 million square km

Since about 30 % of Earth’s surface is land, this means that the total area of land is 0.3 * 515 ≈ 155 million square km, about half of which is habitable for humans. With roughly 7 billion people alive today, we can conclude that there is 0.011 square km habitable land available per person. This corresponds to a square with 100 m ≈ 330 ft length and width.

# The Fourth State of Matter – Plasmas

From our everyday lifes we are used to three states of matter: solid, liquid and gas. When we heat a solid it melts and becomes liquid. Heating this liquid further will cause it to evaporate to a gas. Usually this is what we consider to be the end of the line. But heating a gas leads to many surprises, it eventually turns into a state, which behaves completely different than ordinary gases. We call matter in that state a plasma.

To understand why at some point a gas will exhibit an unusual behaviour, we need to look at the basic structure of matter. All matter consists of atoms. The Greeks believed this to be the undivisible building blocks of all objects. Scientists however have discovered, that atoms do indeed have an inner structure and are divisible. It takes an enormous amount to split atoms, but it can be done.

Further research showed that atoms consist of three particles: neutrons, protons and electrons. The neutrons and protons are crammed into the atomic core, while the electrons surround this core. Usually atoms are not charged, because they contain as much protons (positively charged) as electrons (negatively charged). The charges balance each other. Only when electrons are missing does the atom become electric. Such charged atoms are called ions.

In a gas the atoms are neutral. Each atom has as many protons as electrons, they are electrically balanced. When you apply a magnetic field to a gas, it does not respond. If you try to use the gas to conduct electricity, it does not work.

Remember that gas molecules move at high speeds and collide frequently with each other. As you increase the temperature, the collisions become more violent. At very high temperatures the collisions become so violent, that the impact can knock some electrons off an atom (ionization). This is where the plasma begins and the gas ends.

In a plasma the collisions are so intense that the atoms are not able to hold onto their outer electrons. Instead of a large amount of neutral atoms like in the gas, we are left with a mixture of free electrons and ions. This electric soup behaves very differently: it responds to magnetic fields and can conduct electricity very efficiently.

(The phases of matter. Source: NASA)

Most matter in the universe is in plasma form. Scientist believe that only 1 % of all visible matter is either solid, liquid or gaseous. On earth it is different, we rarely see plasmas because the temperatures are too small. But there are some exceptions.

High-temperature flames can cause a small volume of air to turn into a plasma. This can be seen for example in the so called ionic wind experiment, which shows that a flame is able to transmit electric currents. Gases can’t do that. DARPA, the Pentagon’s research arm, is currently using this phenomenon to develop new methods of fire suppression. Other examples for plasmas on earth are lightnings and the Aurora Borealis.

(Examples of plasmas. Source: Contemporary Physics Education Project)

The barrier between gases and plasmas is somewhat foggy. An important quantity to characterize the transition from gas to plasma is the ionization degree. It tells us how many percent of the atoms have lost one or more electrons. So an ionization degree of 10 % means that only one out of ten atoms is ionized. In this case the gas properties are still dominant.

(Ionization degree of Helium over Temperature. Source: SciVerse)