how can we say that an orbital contains only two electrons?

Question

if in real nobody has seen an electron then how can we say that an orbital contais only two electrons?

Answer 1

You must be one of those people who only believe in things they can tactilely handle. The world of incredibly small objects will be a philosophical challenge, but I'm sure you're up to it.

First, let me give you the short and easy answer:

The entire universe runs on a few very simple mathematical equations. The solution of these equations is extremely difficult, but they perfectly predict and describe physical reality (when solved perfectly), so we're pretty happy with them.

Mathematically speaking, orbitals and electrons exist, and because they exist and have certain properties, they must obey certain rules. One of those rules is that only two electrons can ever fit into the same orbital, and they have to have opposite spin. Any random orbital may have zero, one or two electrons but no more because if you tried to shove a third (or more) electron into an orbital, the orbital would vanish. Think of it this way... its the only way that the elctrons can forever coexist without ever crashing into each other or falling apart in a chaotic state, because electrons (by Coulomb's law) HATE each other and strive to maintain maximum distance from one another while all trying to get close to the positively charged nucleus, which they LOVE.

Now for the long answer:

Before you can accept that two electrons go into an orbital, you need to be able to accept that electrons exist. JJ Thompson is credited with discovery (though not postulation of) the electron in his famous cathode ray experiments. Electrons are evidenced regularly on a macroscopic scale through the use of electricity (the name is not coincidental!) and in such interesting objects as scanning tunneling microscopes and electron microscopes. Robert Miliikan managed in 1901 to measure the charge on the electron in his oil-drop experiments.

An important piece of information came through Ernest Rutherford's (and his students Hans Geiger and Ernest Marsden) experiments on gold foil wherein they demonstrated that the mass of an atom resided in a small region of space in its center, which had a positive charge. Later, Niels Bohr proposed that electrons reside in orbits around the nucleus, which would contain the protons and neutrons (both already demonstrated to exist independently). The usefulness of Bohr's model was widely realized because it could predict experimentally observed phenomena, such as why atomic emission spectra have discrete lines while blackbody radiators give broad spectra.

A key moment in Bohr's theory was the existence of discrete energy states (that is, well-separated) that electrons could exist in. The electrons could change energy levels, but could not occupy any energy states between those energy levels. The idea was hardly unique to Borh, having originated with Max Planck and Albert Einstein in reference to photons; yet its application to the atom was Bohr's own contribution.

This theory was pretty good, but it was a little rough. Many very good physicists decided to work on the combination, including Paul Dirac and Erwin Schrödinger. The final equation describing the behavior of quantum systems (and in particular atomic structure and the resultant properties) is known as the Schrödinger equation. Solution of the Schrödinger equation provides perfect agreement with experiment (i.e. Balmer series of hydrogen) where the solution is exactly possible, and within experimental error where it is not. The Schrödinger equation is a simple, elegant, yet frighteningly hard mathematical equation relating the energy of a system to its wavefunction descriptor (remember, Einstein already showed wave-particle duality):
<Ψ | H | Ψ > = E

Max Born showed that if you multiply the wavefunction ( Ψ) from the Schrödinger equation by itself (i.e. Ψ*Ψ ) you will get a shape that corresponds to the region of space in which electrons that can exist in that level of energy (wavefunction) move as well as the probability of finding an electron in any region of space. In other words, the wavefunction describes an orbital that is fuzzy, not planetary, and determines the particular energy of an electron within it.

What does all of this have to do with two electrons in an orbital? Ultimately, quantum mechanics rests upon six postulates. One of these postulates requires that the product ( Ψ*Ψ ) is real (that is, it contains no imaginary numbers and that Ψ* = - Ψ. A consequence of this postulate is that if you put a particle with spin *up* into a particular wavefunction, the only way the postulates of quantum mechanics (and all of the observations that have been shown to be true thereof) hold is if a spin *down* electron goes in. If you try to put any more than two electrons into the equation, the wavefunction collapses to zero (which means it ceases to exist!).

So to reiterate my first point: the laws of mathematics and the constraints of the physical universe require that elecrons move in defined regions of space around atoms. These regions of space correspond to observable energy changes when electrons move between them. We find it convenient to call the regions of space orbitals. Only two electrons can occupy an orbital because if they tried to fit more they'd destroy the orbital and themselves. The mathematics proves it must be so. I strongly recommend you continue your study of chemistry, physics, and mathematics so that you too can work it all out for yourself to see why we make these absurd claims in the field of quantum mechanics!

Answer 2

By shooting electrons at atoms, and measuring deflection, we can have an idea how big the atom is, including the orbitals. The radius of Helium (2 electrons) is considerably smaller than that of Lithium (3 electrons), but only slightly bigger than Hydrogen (1 electron). This we surmise that the third electron in Lithium is in a different orbital.
Also, comparing the chemical properties of the families of atoms, we a quite certain on the number of outer electrons to be the same down the family (e.g. Li has 1, as does Na, K, Fr, Cs...)

Answer 3

It has to do with magnetic spin and the magnetic fields that result when electron orbitals are filled. Orbitals can only accommodate 2 electrons because the magnetic field produced by the spinning electrons have to be 180* out of phase. If you had three or more electrons, then they cannot simultaneously be 180* out of phase with each other.

Answer 4

Pairs of electrons with opposite spins were used to explain the couplets found in the emission spectra of various elements. Susquent testing and experiments seem to support this conclusion. That being said, we are still working the atomic theory, constantly being updated and revised. If some new evidence comes out where the pairs of electrons don't fit the observations then changes will be made. Until then stick with the best tested explaination.

Answer 5

Who told you that nobody has seen the electrons?

Answer 6

Who sats electrons are not seen? There are methods like elecctron diffraction & x-ray diffraction to see them.

Answer 7

Quantum Physics says so.