Comparison of the Bohr and Quantum Mechanical Models of the Atom
1. In the Bohr Model, the electron is treated as a particle in fixed orbits around the nucleus. In the
Quantum Mechanical Model, the electron is treated mathematically as a wave. The electron has
properties of both particles and waves.
 The Bohr model was a one-dimensional model that used one quantum number to describe the
distribution of electrons in the atom. The only information that was important was the size of
the orbit, which was described by “n” the principle quantum number
 Schrödinger's model (Quantum Mechanical Model) allowed the electron to occupy threedimensional space. It therefore required three coordinates, or three quantum numbers, to
describe the distribution of electrons in the atom.
 In 1926, Erwin Schrödinger combined the equations for the behavior of waves with the
de Broglie equation to generate a mathematical model for the distribution of electrons in an
atom. The distribution of electrons in an atom is called the electron configuration for that
atom. The three coordinates (quantum numbers) that come from Schrödinger's wave equations
are the principal quantum number (n), the angular momentum (sublevel) quantum
number (l), and the magnetic (orbital) quantum number (ml). These quantum numbers
describe the size (energy level), shape (orbital), and orientation (x, y, z plane) in space of the
orbitals on an atom. The electrons are filled in according to a filling order that corresponds (for
the most part) to increasing energy.
 To satisfy the Pauli Exclusion Principle that no two electrons can have the same set of quantum
numbers, a fourth quantum number, the spin quantum number (ms), was added.
2. In the Bohr model, the energy of the electron is described in terms of a definite orbit of definite
energy. In the quantum mechanical model the energy is described in terms of the probability of
locating the electron in a region of space outside the nucleus called an orbital.
3. In the quantum mechanical model, the electron can be very close to the nucleus or very far away.
The probability of the electron being a certain distance from the nucleus most of the time is high
90% (0.529 A for the hydrogen 1s electron).
4. In the quantum mechanical model, energy levels are thought of as clouds surrounding the nucleus
and not fixed orbits.
5. The quantum mechanical model gives information about the location of an electron in an atom,
regarding its energy level, sublevel, orbital, and spin. Every electron has a set of four quantum
numbers, with no two electrons having the same set of four numbers.
Quantum Mechanical Model:
Quantum Numbers: numbers used to give information about the location of an electron in an atom
with respect to its energy level, sublevel, orbital, and spin. Every electron has a set of four
quantum numbers. No two electrons have the same set of four quantum numbers.
1. Principle Quantum Number (n): indicates the main energy level (shell) surrounding the
nucleus or the average distance of the electron from the nucleus. The range of “n” is 1 .
2. Sublevel (angular momentum) Quantum Number (l): represents the shape of the space
occupied by an electron in a given sublevel (s, p, d, f,…) of the principle quantum number
(energy level). The number of sublevels in “n” is equal to n and the range of “l” is 0  n-1.
s
p
d
f
g
h…..
0
1
2
3
4
5
1
3. Orbital (magnetic) Quantum Number (ml): represents the electron’s orientation in space
along the x-, the y-, or the z-axis. There can be a maximum of only two electrons occupying
any one oribital. Any orbital may contain 0, 1, or 2 electrons. The number of orbitals in a
main energy level is n2. The total number of electrons in a main energy level is 2n2.
s sublevels contain 1 orbital, p sublevels contain 3 orbitals,
d sublevels contain 5 orbital, f sublevels contain 7 orbitals,
The number of orbitals in “n” is n2 and the range of “m” is –l  +l
s sublevels contain 1 orbital, p sublevels contain 3 orbitals,
d sublevels contain 5 orbital, f sublevels contain 7 orbitals,
s
0
p
-1, 0, 1
d
-2, -1, 0, 1, 2
f
-3, -2, -1, 0, 1, 2, 3
g
-4, -3, -2, -1, 0, 1, 2, 3, 4
4. Spin Quantum Number (ms): represents the direction of spin of an electron which may be
either +1/2 (), or –1/2 (). There can be a maximum of two electrons occupying any one
orbital. Single electrons have parallel spins and paired electrons have opposite spins.
Writing Electron Configurations:
Filling Order:
1. The quantum atomic model can be compared to an apartment building with different floors,
different apartments on each floor, and different rooms within each apartment.
 Floors in the apartment building are called energy levels or shells and are numbered 1-7
(but may go higher).
 Each energy level (floor) has one or more apartments called sublevels. Sublevels are
apartments of four sizes (rooms) (or more) s, p, d, f,...
 Each room in a sublevel is called an orbital. s- sublevels (apartments) have a single room;
p- sublevels have three rooms; d-sublevels have 5 rooms, and f-sublevels have 7 rooms.
 Each orbital can hold a maximum of two electrons.
Rules Governing Filling Order:
1. Aufbau Principle (building up) – an electron occupies/fills the orbital with the lowest energy first.
2. Hund’s Rule – orbitals of equal energy are filled with one electron each before any one orbital is
filled with a second electron. Spins for single occupied orbitals must be the same (parallel).
3. Pauli Exclusion Principle – No two electrons in the same atom can have the same set of four
quantum numbers. Paired electrons have opposite spins: allows two electrons with opposite spins
to occupy the same orbital.
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Filling Order:
8f…
8s
8p
8d
7s
7p
7d
7f…
6s
6p
6d
6f…
5s
5p
5d
5f…
4s
4p
4d
4f
3s
3p
3d
2s
2p
Spa
1s
Electron Filling Order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p 8s
with maximum number of electrons:
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s25f146d107p68s2
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To write the electron configuration, determine the number of electrons in the element (atomic
number) or ion and fill in using the filling order above. Carbon (Z = 6): 1s22s22p4
However, it is not necessary to memorize this listing, because the order in which the electrons fill can
be read directly from the periodic table.
Methods of Writing
Configurations:
Electron
1) Orbital Notation:
2) Electron Configuration Notation: Al (Z = 13)
1s22s22p63s23p1
3) Shorthand Notation: [Ne]3s23p1
4)
Lewis Dot Diagram (Lewis structure):
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