Comparison of the Bohr and Quantum Mechanical Models of the Atom
1. The electron is treated mathematically as a wave in the quantum mechanical model but as a particle
in fixed orbits around the nucleus in the Bohr model. The electron has properties of both particles
and waves.
2. 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).
3. In the Bohr model, the energy of the electron is described in terms of a definite orbit. 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.
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.
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.”
3. Orbital (magnetic) Quantum Number (“ml”): represents the electron’s orientation in space
along the X-, the Y-, and the Z-axis. There can be a maximum of only two electrons
occupying any one orbital. Any orbital may contain 0, 1, or 2 electrons. The number of
orbitals in a main energy level is n2 and the total number of electrons in an energy level is
2n2.
s sublevels contain 1 orbital, p sublevels contain 3 orbitals,
d sublevels contain 5 orbital, f sublevels contain 7 orbitals,
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 model can be compared to an apartment building with different floors, different
apartments on each floor, and different rooms within each apartment.
2. Electrons are rather peculiar apartment dwellers. They prefer:
a. Floors closest to the ground and the smallest apartments (fewest rooms).
b. They prefer to live one to a room until each room has one occupant. Electrons will then
pair up until each room has two.
c. Each room can hold only two electrons.
d. Apartment buildings have several floors but only the first seven will be occupied.
e. Floors in the apartment building are called shells and are numbered 1-7 (or higher).
f. Each shell (floor) has one or more apartments called subshells. Subshells are apartments of
four sizes s, p, d, f: s-subshell apartments have a single room; p-subshells have three
rooms; d-subshell have 5 rooms; and f-subshell have 7 rooms.
g. Each room in a subshell is called an orbital and can hold a maximum of two electrons.
Electron Filling Order:
8s
8p
8d
8f…
7s
7p
7d
7f…
6s
6p
6d
6f…
5s
5p
5d
5f…
4s
4p
4d
4f
3s
3p
3d
2s
2p

Mall
1s
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s25f146d107p68s2
Rules Governing Electron Configurations:
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 by 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.