Download MODERN QUANTUM THEORY

MODERN QUANTUM THEORY
Werner Heisenberg
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German physicist
1901 – 1976
Leader in the development of quantum theory in the 1920’s
Heisenberg carried out a careful analysis, which showed that it is not possible to determine as
electron’s momentum (mass x volume) and its position/location simultaneously. IF we know one we
cannot know the other. This is known as the Heisenberg’s uncertainty principle: it is impossible to
determine the location and momentum of an electron simultaneously. But electrons can be described as
being located in orbitals, which are 3d spaces where there is a high probability of an electron being
found.
The size, shape and orientation of these orbitals are determined by solving Schrodinger’s wave
equation.
Schrodinger’s wave equation:
The exact solution of the equation yields the four quantum numbers. These numbers are the electrons
‘address’. No two electrons in the atom have the exact same set of quantum number.
Quantum Numbers
Quantum numbers are needed to describe distribution of electron. There are three quantum numbers
needed to this: Principal quantum number, Orbital-shape quantum number or angular momentum
quantum number, magnetic quantum number, spin quantum number.
Principle Quantum number (n)
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Indicated the size of the orbitals since it relates average distance of electron from nucleus in
particular orbital. The bigger the n number the further away from nucleus an electron is.
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The number of electrons in the energy level can be determined 2n2
Orbital-Shape Quantum Number (l)
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Indicated shape/type of orbital
l has possible integral values from 0 to (n –1):
 l=0: s orbital
 l=1: p orbital
 l=2: d orbital
 l=3: f orbital
Principal Quantum
# (n)
1
2
3
4
5
Orbital-Shape Quantum # (l)
Orbital type
Magnetic Quantum Number (ml)
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Indicates the direction/orientation of orbital in space.
Indicates the number of orbitals in a subshell with a particular l value.
Total number of orientations can be calculated using the formula (2l+1).
Orientations can also be used by following this sequence: -l, (-l+1), …0, … (+l –1), +l or more
simply integers from –l to +l.
Spin Quantum Number (ms)
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Evidence for spin was based on the fact that lines of spectra split in the presence of an external
magnetic field.
Electrons act like tiny magnets, as the electrons spin on their own axis it generates a magnetic
field of its own.
In 1924, Stern and Gerlech proved the electron spin nature.
Values are +1/2 or –1/2
Two electrons sharing a single orbital must have different spins (Pauli exclusion principle).