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The Four Quantum Numbers
Principal Quantum Number, n
These are the main energy levels of the electrons that Bohr described. n = 1, 2, 3, 4, …
Diagram: When electrons drop from one level to another they release the energy as a photon of light.
Secondary Quantum number, l
Observation: Albert Michelson in 1891 had found that the bright lines of H were actually composed of more than one line not normally seen with a common spectroscope.
Conclusion: Arnold Sommerfield in 1915 explained this line splitting as additional electron sublevels (subshells, diagram). These quantum subshells relate to the shape of the electron orbitals (s, p, d, f) . The number of subshells is equal to the principal quantum number. (0 to n­1)
eg. n = 3, three subshells (s, p, d) ; n = 2, two subshells (s, p)
Diagram: 1
Magnetic Quantum Number, ml
Observation: Peter Zeeman (1897) observed that when a magnetic field was introduced into the excited gas, the spectral lines further split. Conclusion: The magnetic field affected the energy of the electrons based on their orientation in space. (i.e. x plane, y plane, z plane).
l = 0 à s orbital ­ 1 orientation Diagram:
l= 1 à p orbital ­ 3 orientations
l= 2 à d orbital ­ 5 orientations
l= 3 à f orbital ­ 7 orientations
(# of orientations = ­l to +l)
The Spin Quantum Number, ms
Observation: Some elements and compounds are paramagnetic (a weak magnetic force due to individual atoms rather than to a collection of atoms which is ferromagnetic).
Conclusion: Wolfgang Pauli suggested that electrons have one of two possible spins (clockwise and counterclockwise, +1/2 & ­1/2). Two electrons that are spinning in opposite directions do not create a magnetic force because they cancel each other out. Substances that are paramagnetic have electrons that are not paired with another oppositely spinning electron. This creates a weak magnetic force. The more unpaired electrons present, the greater the paramagnetic force.
For every ml there are two possible electron spins (+1/2 & ­1/2).
diagram: In summary, an electron can be describe based on four quantum numbers:
Eg. 2