why do an orbital should have only two electrons?

according to Pauli' s principle . no two electrons can have same set of quantum numbers



suppose there are 3 electrons , so two electrons will have same spin which is not possible by paulis principle

The filling of atomic orbitals by electrons are governed by the three major guidelines- Aufbau principle; pauli's exclusion principle and Hund's rule.

Aufbau principle : Electrons are filled in various orbitals in the increasing order of their energies.

pauli's exclusion principle : No two electrons in an atom can have all the four quantum numbers identical. Each orbital can accomodate at the most two electrons with opposite spin.

Hund's rule ; This operates when filling orbitals having identical energies. Electrons enter one by one till all of them are singly occupied with parallel spins. This is followed by the double occupation of these orbitals.

As electrons are fermions thus follow Pauli's exclusion priciple.



 

Pauli Exclusion Principle

No two electrons in an atom can have identical quantum numbers. This is an example of a general principle which applies not only to electrons but also to other particles of half-integer spin (fermions). It does not apply to particles of integer spin (bosons).

The nature of the Pauli exclusion principle can be illustrated by supposing that electrons 1 and 2 are in states a and b respectively. The wavefunction for the two electron system would be but this wavefunction is unacceptable because the electrons are identical and indistinguishable. To account for this we must use a linear combination of the two possibilities since the determination of which electron is in which state is not possible to determine.

The wavefunction for the state in which both states "a" and "b" are occupied by the electrons can be written

The Pauli exclusion principle is part of one of our most basic observations of nature: particles of half-integer spin must have antisymmetric wavefunctions, and particles of integer spin must have symmetric wavefunctions. The minus sign in the above relationship forces the wavefunction to vanish identically if both states are "a" or "b", implying that it is impossible for both electrons to occupy the same state.

yaar evr1's tryin 2 explain Pauli's exclusion principle..

Bacha pagal ho jayega,,,

see orbital is a probable area of finding electrons..

And when these electrons spin and revolve,, they change their energies and keep changing their spins also..

Now at a time ,, in an orbital there are two opposite spins, to maintain minimum energy, and no more electrons can be found in orbital, because then there can be instability due to electric winds...

This was observed, and Pauli made it his rule .. On soon existence of quantum mechanics,, it was explained with help of quantum numbers,, as given by Mr. Edison