State the Pauli Exclusion Principle

According to Pauli Exclusion Principle, No two electrons can have samples values of the quantum numbers n, l,m_l and m_s or they can not have all these quantum numbers similar; at least one of the four numbers which are strictly required to Specify the state of an electron should be different from the quantum numbers which specify the state of another electron of the same atom.

When we consider the electron spin l_a single electron can be represented by the four quantum numbers. The principal quantum number n can take integral Values 1,2 ……….( n = 1). The magnetic quantum number m_l represents the component of l along the axis of a magnetic field and can take on all integral values between l and -l. Finally, the spin quantum number m represents the component of the spin angular momentum along the axis of the field can take only + 1/2 and – 1/2 values.

From the energy consideration, it seems that all the electrons in an atom should occupy a state of at least energy n=l and l=0. If this is so, the building up of the periodic system and the periodicity in the properties of the atoms and in the energy level diagram cannot be explained.

An important principle known as Pauli’s exclusion principle prevents the filling of the various shells with an arbitrary number of the electrons. It states that in one of the same atom, no two electrons have the same sets of the values for the four quantum numbers  n, l,m, and m_s :
Let us consider the electronic structure of some of the elements in the light of this principle of Pauli. The hydrogen atom has only one electron revolving around a proton. The electron occupies an orbit of the lowest energy when in the normal state. Therefore, n =1 and so l = 0. We understand from the that m_l = l ………l, so  m_l= 0 . Magnetic spin quantum m_s will be equal to + 1/2.

Spectroscopically this electron is represented as l S’ where S shows that l = 0 and superscript give the number of the electron in this stage.

For helium, the nuclear charge increase to two and a second electron is introduced. The set of the quantum number associated with the second electron must be different from that from the first electron as described in Pauli’s principle so we can make n=0 , l = 0 ,m_l  = 0, but the spin must be different so that ms = – 1/2.

The K shell is full and is represented as IS². The innermost shell is called K shell whereas the outer shells are named L,M,N —-in spectroscope notation. Lithium is constructed from helium by increasing the nuclear charge to three and making the outer electrons three so as to make the atom electrically neutral. The third electron will have n = 2 and the quantum numbers assigned to it accordance with the least energy considerations are n=2 , l=0, m_l =0, and the ms = + 1/2 so that the configuration is 1S² ,2S² .this process by adding electrons yields a remarkable way for the periodic system of the element.