Download The Quantum Mechanical Model

Ch. 5 Electrons in Atoms Notes
The Bohr Model:
 Bohr proposed that an electron is found only in specific
circular paths, or orbits, around the nucleus.
 Each possible e- orbit has a fixed energy.
 The fixed energies are called energy levels.
 To move from one energy level to another, an e- must gain or
lose just the right amount of energy.
 Higher energy levels are generally farther from the nucleus.
 Quantum = the amount of energy required to move an
electron from one energy level to another energy level.
 Bohr’s model worked great to explain Hydrogen, but failed to
explain the energies absorbed and emitted by the other atoms.
The Quantum Mechanical Model:
 De Broglie proposed that moving particles like electrons have
some properties of waves.
 Schrodinger (Austrian physicist) used a mathematical
equation to describe the motions of electrons.
 Quantum Mechanical Model = The modern description of the
e- in atoms, based on Schrodinger’s work.
 Like the Bohr model, the quantum model predicts quantized
energy levels for electrons, however it does not describe the
exact path the electron takes around the nucleus.
 It is concerned with the probability, or likelihood, of finding
an electron in a certain position.
 The main difference between Bohr’s model and the quantum
mechanical model is the electron orbitals. Bohr’s orbitals
were circular and fixed. In the quantum mechanical model
the electron orbital are regions in space where the electron is
likely to be found.
 The quantum mechanical model is
often called the “electron cloud model”
(fuzzy boundaries of e- orbits)
Quantum Numbers
1) A quantum number is used to define the energy and location
of an electron in the quantum mechanical atom.
2) A total of four quantum numbers are necessary to completely
define the energy and location of an electron.
3) The first three numbers give the location of the electron.
4) The fourth quantum number describes the orientation of an
electron in an orbital.
First Quantum Number
1)
2)
3)
4)
5)
Principal quantum number
n = 1,2,3,4,… (positive integer starting with 1)
Describes the energy level that the electron occupies.
Basically tells you how far the electron is from the nucleus.
Generally, the larger the value on n, the farther away from
the nucleus and the higher the energy of the electron.
n =1
n =2
n =3
Second Quantum Number
1. Describes the shapes of atomic orbitals.
2. l = 0, 1, 2 , 3
s, p, d, f
3. Orbital s = sphere
p = dumbbell d and f = complex
Shapes
4. Each principal energy level can have a maximum of one s
orbital (2e-), three p orbitals (6e-), five d orbitals (10 e-), and
seven f orbitals (14e-). Within each principal energy level, the
group of same shape/energy orbitals is a sublevel.
5. Sublevels
one s
three p
five d
seven f
orbital
orbitals
orbitals
orbitals
Third Quantum Number
6. Magnetic quantum number (ml)
7. Tells you the electron position by designating the orientation
in space of the orbital that is occupies.
8. Ex: p orbital can have three spatial orientations. (x,y,z)
Fourth Quantum Number
1. Spin quantum number(ms )
2. Labels the orientation of the electrons within the orbital (the
direction of spin)
3. Clockwise & Counter clockwise. 
No two e- have an identical set of four quantum numbers.
The principal quantum number always equals the number of
sublevels within that principal energy level.
1
2
3
4
1s
2s & 2p 3s, 3p, & 3d 4s, 4p, 4d, 4f
Electron Arrangement in Atoms
 In the atom, electrons and the nucleus interact to make the
most stable arrangement possible.
 The ways that electrons are arranged into various orbitals
around the nucleus are called electron configurations.
The Aufbau principle: Electrons occupy orbitals of lowest
energy first.
 Within each principal energy level:
Lowest-energy
s<p<d<f
highest-energy
 The range of one principal energy level can overlap another
level, so the electrons fill the orbitals in the following order,
according to energy:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p
Pauli Exclusion Principle-An atomic orbital may describe,
at most, two electrons. In order to occupy the same orbital, two
electrons must have opposite spins. 
Hund’s rule: When electrons occupy orbitals of equal energy
(the same sublevel), one electron enters each orbital until all the
orbitals contain one electron with the same spin direction.
 Electrons spread out as much as they can with one electron in
each orbital, until all of the orbitals have one electron. Second
electrons then occupy each orbital so that their spins are paired
(opposite) with the first electron in the orbital.
EX: 3p  
3p   
w/ 2 e-
w/4 e-
How To Write Electron Configurations
Shorthand method of showing the e- arrangement.
1. Determine how many electrons are in the atom?
 What is the atomic number?
Ex: Ga has 31 e- because its atomic # is 31. O has 8 ebecause its atomic # is 8.
 Is it an ion? If so, subtract the charge from the atomic
number.
Ex: Mg2+ has 12 – 2 = 10 e ;O2- has 8 - ( -2) = 10 e2. Fill orbitals in the proper order w/ e- .
 Order of increasing energy
 Use the Aufbau diagram at first. 2 electrons can fit in each
box = orbital.
 Only the highest energy orbital can be partially filled.
Ex: Chlorine has 17 e- so its configuration is
1s22s22p63s23p5
3) Check that the total # of e- (superscripts) in the econfiguration equals the # of e- in the element.
Ex: In the above example (2+2+6+2+5 = 17)
Electron Energy Level Diagram
 Box & Arrow Notation = use labeled boxes to represent each
orbital and an arrow to represent each electron.
 Be sure to follow Hund’s Rule
 EX: Phosphorus
Valence Electrons
 Valence e- are the outermost electrons-electrons with the
highest principal quantum number.
 Valence e- will only include s & p orbitals, because they will
always have the highest principal quantum number.