## Azimuthal Quantum Number

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# Azimuthal Quantum Number

It refers to the subshell or sublevel to which an electron belongs and describes the motion of the electron. The magnitude of the angular momentum of an electron (angular velocity x moment of inertia) is related to by the expression:

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This means that the values of for the subshells of a shell are govermedby n. When n=1, there is only one subshell with the value . When n=2 there are two subshells with the values =0. 1. when n=3 there are three subshells that have values =0,1,2. Similarly, when n=4.. no. of subshells=4 with values = 0,1,2,3. For every value of . there is a separate notation to indicate subshell. For example.

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**where =0,1,2,3,........,(n-1).**This means that the values of for the subshells of a shell are govermedby n. When n=1, there is only one subshell with the value . When n=2 there are two subshells with the values =0. 1. when n=3 there are three subshells that have values =0,1,2. Similarly, when n=4.. no. of subshells=4 with values = 0,1,2,3. For every value of . there is a separate notation to indicate subshell. For example.

Quantum No. =0 1 2 3 4____ 5.... Subshell Notation =s P d f g____ h.... |

The first four notations :s,p,d and f are adjectives used earlier to identify spectral lines; sharp , principal, diffuse and fundamental but subsequent notations used for >3 proceed alphabetically : g,h.i.j. ...so on.

Knowing the value of n and finding out , we designate a subshell. For example, subshell for n=1,=0 is called is subshell and others are given in the form of a table

n________________ _________________Subshell notation |

2________________ {0_____________________2s _______________ 1______________________2p |

3 ______________ {0_____________________ 3s ________________ 1_____________________ 3p ________________ 2 _____________________ 3d |

4________________ {0_____________________ 4s _________________ 1_-____________________4p _________________ 2-____________________ 4d ________________ 3___-------_----------------------- 4f |

For atoms other than hydrogen, the energies of subshells within a given shell increases slightly with increasing. For example, for n = 3, has values 0,1 and 2 with subshell notation 3s, 3p and 3d, repeetively. For H atom , the subshell energies are equal.

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But for other atoms, the energy increases with increasing , that is :

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