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Arrangement of Electrons in Atoms
Chapter 4



Quantum Numbers and Atomic Orbitals
Chapter 4.2


Quantum Theory - describes mathematically the wave properties of electrons and other vary small particles (Schrodinger)

Atomic Orbital - area where an electron can be found

Quantum Numbers - are numbers that specify the properties of atomic orbitals and their electrons.

The 1st 3 Quantum Numbers indicate the region occupied by a given orbital in terms of:
  • 1. Distance from the nucleus
  • 2. Orbital shape
  • 3. Orbital position with respect to the 3 dimensional x, y, and z, axes


Whole numbers and relate to each other.

The 4th quantum number has only 2 values and is needed to specify one of two possible orientations of and electron within an orbital.

Principal Quantum Number - symbolized by n, indicates the main energy levels surrounding a nucleus.
  • Energy levels - can be called shells
  • n value is a whole number (1,2,3)
  • (n=1 main energy level - closest to the nucleus
  • As n increases - distance of main energy level form nucleus increases - their energy increases


Orbial Quantum Number - indicated the shape of an orbital
    *each main energy level - different shapes - occupy different regions
    * regions are called sublevels or subshells
table 4.1 p 109

The number of sublevels = the principal quantum number
    1st 4 numbers - s, p, d, f
    s - lowest enrage level, spherical in shape
    p - dumbbell shape
    d - dumbbell shape - 4 lobes
    f - very complex

Number of Sublevels in each energy level:

1st energy level - 1 sublevel - s
2nd energy level - 2 sublevels -s,p
3rd energy level - 3 sublevels - s,p,d
4th energy level - 4 sublevels s,p,d,f
n = the # of sublevels

Magnetic Quantum Number - indicates the orientation of an orbital about the nucleus
    s sublevels - possible orientation - only 1 s sublevel in each energy level
    p sublevels - 3 different orientations - (x, y, z) - each sublevel contains 3 different p orbitals - p p p
    d sublevels - 5 different orbitals in each d sublevel, table 4.16 p. 110
    f sublevels - 7 different orbitals in each f sublevel

The # of orbitals in each main energy level equals the square of the principal quantum number (table 4.1)

Spin Quantum Number - has only 2 possible values (+ 1/2 or - 1/2) - which indicate 2 possible states of an electron in an orbital.

  • Each electron spins, similar to the earth - creating a north and south pole
  • One spins in one direction, the other spins in the opposite direction



Each orbital can hold up two electrons - having opposites spins.
    1st energy level - 1 s orbital - contain 2 electrons - one sphere
    2nd energy level - 1s orbital - 2 electrons - 3p orbitals - 6 electrons - total 8 electrons
    3rd energy level - total 18 electrons

 		 
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