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Bohr model
1. Electrons revolve around nucleus in circular paths,
like planets around the sun. He called these paths
2. Each orbit has a specific energy and any electron in
that orbit has that energy.
3. Orbits are therefore also energy levels. The closer to
the nucleus, the lower the energy. Energy levels are
numbered 1, 2, 3, etc., with one the closest to the
4. Electrons can jump from one orbit to another, but not in
between. In order for this jump to take place, energy has
to be absorbed (going from low to high) or emitted
(going from high to low)
This last point explains absorption and emission spectra.
Each possible jump will correspond to a specific energy and
only that energy, which will correspond to a specific
wavelength of electromagnetic radiation. Every element has
slightly different values for their energy levels. Also, different
atoms have different numbers of possible jumps.
Bohr also showed that when an electron moves from one
energy level to another, the energy emitted or absorbed
follows the equation:
1 1
E  h  R H ( 2 - 2 )
ni nf
RH is called the Rydberg Constant and has a value of 2.18 x
10-18J, and ni and nf are the initial and final Bohr energy
levels. They are always integers. In the lab, you will do an
experiment where the Rydberg constant is given a different
value. The lab value incorporates h into the constant value,
but we still call it the Rydberg constant.
Not only does light have a dual nature, but so does all
matter. It is only noticeable with very small particles, like the
electron. In 1924, Louis de Broglie provided a mathematical
explanation, which we won’t worry about. It is important to
us only to show that photons are not unique, but that all
matter is subject to the same rules of Nature.
Although, the Bohr Model worked very well (actually exactly
for the H atom) and was readily accepted as an advance in
our knowledge of atomic structure, there were some
theoretical problems that he could not really explain.
It wasn’t until 1923, when a physical chemist, named Irwin
Schrodinger, proposed a new model for the atom. This
model is called the Quantum Mechanical Model. It is
purely a mathematical model, but we can use the Bohr
model with some liberal modifications, to help understand
this model. Once again, like the Bohr Model, it can be
solved exactly for the H atom, but not for multi-electron
systems. However, we apply the assumptions for the H
atom to any system, assuming that the differences will be
Basic Assumptions:
1. Energies of electrons can have only specific values
- similar to Bohr Model - quantized energies of
2. Position cannot be specified - only most probable
average position can be calculated
3. The solution of the mathematical Equation, called the
Schrodinger Equation, requires certain values, called
quantum numbers. There are 4 of these. They can
only have certain restricted values, hence the term
quantum numbers. Every electron in an atom has a
set of these 4 quantum numbers, in order to
completely describe its energy, as accurately as we
Orbital - a part of a sublevel that actually contains the
electrons (like cars on a road) - can hold a maximum of 2
The Principle Quantum Number – n:
Describes the main energy level (like Bohr’s energy
levels). It can only have positive integer values (1, 2,3 etc).
Like the Bohr Model Energy Levels, the higher the n value,
the higher the energy and the further away from the nucleus.
The Angular Momentum Quantum Number – (l):
Describes the shape of the orbitals. Also describes
the energy of sublevels to the principle energy level. The
values of l are dependent on the value of n. For each value
of n, l can have integer values from 0 to n-1. Chemists have
found it convenient to assign letters for each different l value:
l value
Letter Symbol
The lower the value, the lower the energy.
The Magnetic Quantum Number – (ml)
Describes the orientation of an orbital in space. Also
describes the energy of the electron, if it is subject to external
magnetic fields. In ordinary situations, the energy of the
electron is the same for all values of ml corresponding to a
certain l value. ml values are restricted to all integers,
including 0, from – l to + l
The Electron Spin Quantum Number - (ms)
Essentially describes the direction of spin for the
electron (clockwise or counterclockwise). Enables 2
electrons to occupy the same orbital. Has no effect on the
energy of the electron unless there is an external magnetic
field. Can have values of + ½ or – ½ .
Examples: If n = 1, then l = 0, ml = 0 and ms = + ½ or – ½ .
Frequently abbreviated as (1,0,0,+ ½ ) or (1,0,0, - ½ ).
If n =3, then l can be 0, 1, or 2. The values of ml
depend on which
l value we refer to: for 0, then ml can only be 0; for l = 1, ml
can be -1, 0 or +1; and for l = 2, ml can be -2,-1,0,+1 or +2.
Each different ml represents a different orbital and each orbital
can have ms values of + ½ or – ½ . Thus for n = 3, there are 9
possible different orbitals.
# of orbitals
Maximum #
-2,-1,0,+1,+2 5
Orbital Shapes: