Chemists and physicists use four quantum numbers to describe the position of any electron around a many electron atom.
  • The first quantum number termed the principal quantum number (symbol n) describes the energy level that the electron can be found in. It measures the average distance of the electron from the nucleus.
    • These are often termed shells. Each shell is at an increasing distance from the nucleus and electrons that occupy these higher levels have increasing amounts of energy. Values of n vary from 1 - 7
    • The concept of energy levels was first proposed by Neils Bohr to explain problems that Ernst Rutherford encountered with his model of the atom. Bohr proposed that electrons moved in stable orbits or shells and when exposed to energy, the electron absorbed the energy and moved to higher orbits further from the nucleus. After a short time they released the energy they had absorbed and moved back to lower orbits. The shell or orbit that they occupied of lowest energy was termed their ground state.

    Diagram #1
picture of energy levels To the left we see the first four shells that exist about the nucleus , n =1 - 4. Note they are also labeled K,L,M,O. To the right we see an electron releasing energy in the form of red light as it moves from n =3 to n = 2, and blue light as it moves n=3 to n=1.
electron moving between energy levels


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Assignment #1
Atomic Scientists



The second quantum numbertermed the orbital quantum number (symbol l) describes the shape of the orbital that an electron will occupy.
  • Values of l vary from 0 to 3.
  • These are often termed energy sublevels and each sublevel has slightly different energy .
  • the four sublevels are s(l = 0), p(l = 1), d(l = 2), f (l = 3) each with it's own shape.
  • The number of possible values of l equals the value of n. Therefore the first energy level has 1 sublevel, the second 2, until a maximum of 4 is reached.
  • The orbitals can have four shapes. They are the s shape, which looks like a sphere(see below ), the p orbital which looks like a dumbbell seen in diagram #3, the d orbital that looks like a propeller, and an f orbital that has many lobes.
    Diagram #2
    1s orbital


The third quantum number is termed the magnetic quantum number( symbol ml )
  • this quantum number identifies the direction the electron orbital has around the nucleus (it's orientation in space)
  • it indicates the # of each type of orbital within a level.
    • One s orbital
    • three p orbital
    • five d orbital
    • seven f orbital
  • the different orientations causes little or no difference in energy for the electrons
  • the number of orbital at a level = n 2(Example if n = 2 there are two orbital types with a total of 4 orbital present 1 s and 3 p orbital). The graphic below represents the three possible p orbitals that can exist at a level.
Diagram #3
    three different p orbitals The graphic on the left represents the three possible p orbitals with different orientations that can exist at a level (starting at n = 2). The graphic on the bottom right represents the three together about the nucleus.

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    Assignment #2
    Orbital Principles


The fourth and final quantum number describes the spin of the electron and is given the symbol m s. Scientists have determined that the electron can spin in either a clockwise (+) or counterclockwise(-) direction within an orbital. This means that an orbital can only contain two electrons.
  • Therefore
  • s orbital (1) hold 2 electrons
  • p orbital (3) hold 6 electrons
  • d orbital (5) hold 10 electrons
  • f orbital(7) hold 14 electrons.
  • Electrons in the same orbital with opposite spins have essentially the same amount of energy.
The chart below summarizes the information about orbital (sublevels).
Table #1
Orbital Shape
Energy level (n) in which it is first found
Number of orbital at a level
Number of electrons in these orbital
s(sphere)
1
1
2
p(dumbbell)
2
3
6
d(propeller)
3
5
10
f(many lobed)
4
7
14