**Quantum Numbers**: They define:

The volume of space (orbital) where there is maximum probability of finding the electrons.

The energy of each orbital

The shape of each orbital

The direction of each orbital

**Principal quantum number (n)**: Used by Bohr in explaining the spectrum of the hydrogen atom.It describes:

The size of the principle energy levelValues of n are 1, 2, 3, 4, and so on - Cannot be zero

The energy of the principle energy level

The order of the principle energy level or electron shells (7 shells in the heaviest atom)

Every principle energy level divided into no. of energy sublevels

**The number of electrons required to fill a given energy level = 2n2**

Examples:

The 1st shell saturated by (2x12) = 2 electronsThe 2nd shell saturated by (2x22) = 8 electrons

The 3rd shell saturated by (2x32) = 18 electrons

The 4th shell saturated by (2x42) = 32 electrons

The 5th, 6th, 7th shells doesn't obey this law because the atom becomes unstable if no. of > 32 electrons

**Subsidiary quantum number (l) (azimuthally)**: Shown by Summerfield when he used a spectroscope, he found that the single spectral line is indeed a number of fine spectral lines representing electron transition between very near energy levels (sublevels)It describes:

The shape of each energy sublevels within each principle energy levelCan be any integer between 0 and n – 1 (less than n)

The energy of each energy sublevels within each principle energy level

The number of energy sublevels within each principle energy level

The (s) orbital are spherical (l = 0)

The (p) orbital are polar (l = 1)

The (d) orbital are clover-leaf shaped (l = 2)

The (f) orbital are complicated (l = 3)

For n = 1, (l) can be 0 (1s)Magnetic quantum number (m): It describes:

For n = 2, (l) can be 0, 1, and 2 (2s, 2p)

For n = 3, (l) can be 0, 1, and 2 (3s, 3p, 3d)

The orientation of each orbitals within each energy sublevelCan be any integer between - l and + l

The number of orbitals within each energy sublevel

For s: (l) = 0 (m) = 0 No. of orbitals for (s) = 1Spin quantum number (ms):

For p: (l) = 1 (m) = -1, 0, 1 No. of orbitals for (p) = 3 (Px, Py, Pz)

For d: (l) = 2 (m) = -2, -1, 0, 1, 2 No. of orbitals for (d) = 5

For f: (l) = 3 (m) = -3. -2, -1, 0, 1, 2,3 No. of orbitals for (f) = 7

It Detect:

The direction in which the electron spin around its axis during its rotation (clockwise or anti- clockwise) in order to form 2 opposite magnetic fields to decrease the repulsion force between the 2 electrons.

It has only two possible value (+ 1/2 OR - 1/2 )

## 1 comments:

thank you :)

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