Dr. S. B Maulage Dept of Chemistry

THE QUANTUM NUMBERS The 4 quantum numbers are like a zip code for the electron.

They specify an atomic orbital, a region in space where there is high probability of finding an electron with a characteristic energy, and the number of electrons which can occupy the orbital.

The Principal Quantum Number – n The modern equivalent of n in the Bohr Theory. It describes the main energy level. It can have the values of the positive integers: 1, 2, 3, 4, 5,.... It is related to the average distance of the electron from the nucleus. The energy of the electron depends principally on n. Orbitals of the same quantum number n, belong to the same shell.

B) Angular momentum quantum number - azimuthal or subsidiary quantum number - distinguishes orbitals of a given n having different shapes. Other synonyms are sublevel and subshell. There are n different kinds of orbitals each with a distinctive shape denoted by .

 has values from 0 to n-1. (It is important to remember that in this case 0 does not mean nothing.) When n = 1,  can only equal 0 - only one subshell When n = 2,  can equal 0 and 1 - two subshells When n = 3,  can equal 0, 1, and 2 - three subshells

Associated with each value of  is a letter related to a shape which is a region of space with an approximate 90% occupancy rate by an electron of a specified energy. When = 0, the letter designation is s and the shape is spherical. When = 1, the letter designation is p and the shape is dumbbell shaped. When  = 2, the letter designation is d and the shape is a cloverleaf and another shape.

designations used are 1s, 2s, 2p, 3s, 3p, 3d,...

C) m  is the magnetic quantum number which distinguishes orbitals of given n and . It specifies the orientation in space of the atomic orbital. The number of different orientations in space depends on the subshell designated. The allowed values are integers from -  through 0 to +  giving 2  +1 possibilities. When n = 1;  = 0; m  = 0 - only 1 orientation possible - a sphere.

When n = 2;  = 0; m  = 0 - only 1 orientation possible - a sphere. When n = 2;  = 1; m  = -1, 0, +1 - 3 orientations are possible – one dumbbell along each of the three axes, x, y and z.

When n = 3; = 0; m  = 0 - only 1 orientation possible - a sphere. When n = 3; = 1; m  = -1, 0, +1 The 3 orientations which are possible are one dumbbell along each of the three axes, x, y, z. When n = 3; = 2; m = -2 -1, 0, +1 +2 There are 5 orientations possible – four cloverleafs and 1 other shape. One is along the xy axes, three between the axes, and the special one is along the z axis.

D) ms is the spin quantum number D) ms is the spin quantum number. An electron has magnetic properties that correspond to a charged particle spinning in its axis. Either of 2 spins are possible??? 2 values are possible - +½ and -½ for every set of n,  , m  - this gives two as the number of electrons which can occupy each orbital. 2 e's in the 1s orbital - "zip code" 1,0,0,+ ½ and 1,0,0,- ½ .

2 e's in the 2s orbital - "zip code" 2,0,0,+ ½ and 2,0,0,- ½ . 2 e's in each 2p orbital - "zip code" 2,1,-1,+½; 2,1,-1,- ½; 2,1,0,+ ½; 2,1,0, -½; 2,1,+1,+ ½; 2,1,+1- ½ .

CAPACITIES OF PRINCIPAL LEVELS, SUBLEVELS, AND ORBITALS A) Each principal level of quantum number n can hold 2(n2) electrons. level 1 can hold 2e (2 X 12) level 2 can hold 8e (2 X 22) level 5 can hold 50e (2 X 52)

B) Each principal level of quantum number n can contain a total of n sublevels. level 1 has 1 sublevel - s level 2 has 2 sublevels - s and p level 3 has 3 sublevels - s, p, and d level 4 has 4 sublevels - s, p, d and f

C) Each sublevel of quantum number  can contain a total of 2  + 1 orbitals. = 0 there are (2 x 0 + 1) orbitals, 1 orbital called s.  = 1 there are (2 x 1 + 1) orbitals, 3 orbitals called p.  = 2 there are (2 x 2 + 1) orbitals, 5 orbitals called d. D) Each orbital can contain only 2 electrons.

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