Lecture 02.; spectroscopic notations by Dr. Salma Amir

spectroscopic notations , quantum numbers,

1. Lecture No. 02 Couse title: A tomic Spectroscopy T opic: Spectroscopic Notations Course instructor: Dr. Salma Amir GFCW Peshawar

2. Spectroscopic Notations Spectroscopists of the late 19 th and early 20 th century created a system of spectroscopic notation to describe the observed line spectra . Quantum numbers were invented to provide an quantitative description of observed (and unobserved) transitions. These together provide a short-hand description of the state of the electrons in an atom or ion . The spectroscopic notion is a method of describing the quantum state of an atom using the principal quantum number, the orbital quantum number and the total angular momentum quantum number. The total angular momentum can be determined by taking the sum of the orbital quantum number and the spin quantum number.

3. Quantum Numbers Four quantum numbers suffice to describe any electron in an atom. These are: n , the principal quantum number ., n takes on integral values 1, 2, 3, ... . l , the azimuthal quantum number ., l takes on the integral values 0, 1, 2, ... , n -2, n -1. m , the magnetic quantum number . m takes on the integral values - l , -( l -1), ..., -1, 0, 1, ..., ( l -1), l . s , the spin quantum number . This describes the spin of the electron, and is either +1/2 or -1/2.

4. Quantum Numbers for Atoms As with electrons, 4 quantum numbers suffice to describe the electronic state of an atom or ion. L is the total orbital angular momentum. L corresponds to the term of the ion (S terms have L =0, P terms have L =1, etc.). In the case of more than one electron in the outer shell, the value of L takes on all possible values of L=Σ l i The quantum number S is the absolute value of the total electron spin, S = Σ s i . Each electron has a spin of +/- 1/2. S is integral for an even number of electrons, and half integral for an odd number. S =0 for a closed shell. J represents the total angular momentum of the atom of ion. It is the vector sum of L and S . For a hydrogenic ion, L =0, S =1/2, and J =1/2. For more complex atom, J takes on the values L + S ……. L - S , M , the Magnetic quantum number, takes on values of J , J -1, ..., 0, ..., - J -1, - J .

5. Spectroscopic notations The atomic level is described as n 2 S +1 L J or 2 S +1 L J where S , n , and J are the quantum numbers defined earlier, and L is the term (S,P,D,F,G, etc ). 2 S +1 is the multiplicity The   multiplicity  of a term is given by the value of 2 S +1. A term with  S =0 is a singlet term;  S =1/2 is a doublet term;  S =1 is a triplet term;  S =3/2 is a quartet term, etc.

6. Spectroscopic notation for Helium (He) No. of electrons=2 Electrons in ground state S= s 1 +s 2 = ½-½=0 2S+1= 1 (Singlet state) L=0 for electron in s orbital J=L+S= 0+0=0 Spectroscopic notation= 2 S +1 L J 1 S o Electrons in excited state (1s and 2s) S= s 1 +s 2 = ½-½= S= s 1 +s 2 = ½+½=1 2S+1= 1 (Singlet state) and 2S+1 = 3 (Triplet state) L=0 for electron in s orbital J=L+S= 0+0=0 J=L+S= 0+1=1 Spectroscopic notation= 2 S +1 L J 1 S o , 3 S 1