Elerium, otherwise known as element 115, is the energy source for all alien technologies. Mined from reserves near Cydonia, it has a variety of uses. However, it cannot be found on Earth...
Elerium cannot be synthesized on Earth; it can only be obtained from UFO Assaults or Alien Base Assaults. Elerium is housed within UFO Power Sources, and is very fragile. If upon starting a UFO assault you find a UFO Power Source to have been destroyed (as a result of a crash landing), its Elerium will surely have been destroyed as well. Be careful about using explosives near intact UFO Power sources, as the Elerium within is easily toasted!
At the end of a successful mission, any Elerium contained within intact UFO Power Sources will be automatically collected and returned to your base. If for some reason you need to end a mission prematurely, you can still collect Elerium by hand, by shooting open a UFO Power Source (generally with a plasma weapon). For more on securing Elerium in this way, see UFO Power Sources.
Perhaps the most efficient way to gain a stock of Elerium is to find an Alien Base and attack the Supply Ships as they land nearby. Leave the base intact to attract more supply ships, as the Elerium is worth more than the score penalty (150 units per intact Supply Ship).
UFO Power Sources can also be found in some Alien Bases, if they have a particular base "module". You can raid such a base without having to win the mission, and have a soldier carry the Elerium back to the entry lift and then abort (see Alien Base Assault#Smash And Grab for more details). Attacking the base's Supply Ships is likely to be a safer and more reliable source of Elerium, however; see UFO Recovery Values#Alien Base Assaults for more details.
On the map, Elerium appears as a purple ball (the same graphic as a Stun Bomb on the ground). This object is worth 50 points of Elerium. During Base Defense, some of your own Elerium from stores may appear on the battlescape. This is a Good Thing™ if you win the mission, as each unit is represented as a pod and can be recovered for fifty units. This is probably a bug and appears to be absent from the Collector's Edition.
Don't sell Elerium. Although you do have the option to do so, this is to be highly discouraged. It is used to fuel the Firestorm, the Lightning, and the Avenger. It is also used, in varying amounts, to manufacture most Alien Artefacts, Flying Suits, and various other technologies. Given that you can only obtain Elerium in the battlefield, selling it is not a good idea. If you choose to, it will fetch you $5,000 per unit.
Elerium In Reality
Ununpentium, the temporary name for synthesized element 115, was only created briefly in atomic laboratories in 2004 and is not the subject of much research. However UFO 'researcher' Robert Lazar made several claims about E-115 in the 1980's. For example, it would be the only element that had a gravitational field extending past it's own atomic 'shell'. This deviance from the normal rule would be so significant that perhaps the technologies seen in the X-Com Series could become a reality - anti-gravity devices used for both flight and particle acceleration.
How much Elerium is “1 Elerium“?
Since some information about the physical laws that rule Elerium-related technology is given in the game this question can be answered to some extend. To fit Elerium into the laws of physics, some basic facts have to be “chosen”. The only way to equal an amount of Elerium to an amount of power is to calculate the power needed by Elerium-propelled crafts. I chose the “Avenger” for this calculation. Since it is the most advanced craft built by X-Com we can assume it has maximum efficiency, which eases the maths a bit.
I also assumed that the weight of the Elerium item that can be picked up in combat (3 weight units) can not be used to deduct the actual mass of Elerium in this item.
First we have to find the “Avenger”s maximum speed in SI units.
r * f / t = v
With r as range (54000 nautical miles), t as time that the craft needs for that range (10 hours) and f as factor translating nautical miles into kilometres (1.852) the maximum speed v is almost exactly 10,000 km/h.
The required power for maintaining this speed can be deducted solely from atmospheric drag.
F = v^2 * RHO * A * C_d /2
P = F*r
With v as velocity (10,000 km/h), RHO as density of atmosphere (see below), A as area where the drag applies to the craft (for the “Avenger” this would be roughly estimated 20 m^2), C_d as drag coefficient (since the “Avenger” should be constructed quite well I estimated 0.3) and r as range in kilometres (100000), F is the force applied by atmospheric resistance and P the total power over total range that is used to overcome this resistance.
I took 5000 ft. as average flight height to estimate the atmospheric density. This means that RHO roughly equals 0.85.
The velocity has to be [m/s] and the range has to be [m] to fit for the following formulas.
Therefore follows: F = 1.968 * 10^7 kN and P = F * 10^9 = 1.968 * 10 ^16 kNm
Now we take that keeping the craft at max speed only uses 75% of required energy per mission, since combat situations as well as turning, starting and landing (overcoming inertia) use extra power. Now we use Einsteins most popular formula to calculate the required mass from our power requirements:
1,968 * 10^16 / 0.75 = m´ * c^2
Therefore follows: m´ = 291.555 g
Taking into account that “only” 99% of mass is converted into energy:
m = 291.555 / 0.99 = 294.5 grams , which is the mass carrying the “Avenger” for 100.000 kilometres!!!
Since an “Avenger” is fuelled with 12 units of Elerium, one unit weights roughly 25 grams, which means one UFO power source carries about 1.25 kilogram of Elerium. This also means that the explosions of UFO Power Sources after crashing are BY FAR too small. An explosion in which less than 0.1% (around 1 gram) of the contained Elerium is transformed into energy would have twice the explosive force of the Hiroshima Atomic bomb. Using this model, shooting down a terror ship with 4 power sources destroyed would explode with a force of almost 90 kilotons, enough to completely destroy a small city. And keep in mind: An alien grenade contains 25 grams of Elerium, which using the same assumed conversion rate, gives it a explosive force 36 times that of a MOAB 'Super Bomb'.