Module 9: Quantum Theory and The Electronic Structure of Atoms presentation

About This Presentation

Title:

Module 9: Quantum Theory and The Electronic Structure of Atoms

Description:

Bohr made significant contributions to the understanding of atoms, including the ... In orbital diagrams, orbitals are represented by lines and electrons are ... –

Number of Views:294

Avg rating:3.0/5.0

Slides: 40

Provided by: MDC1

Category:

more less

Transcript and Presenter's Notes

Title: Module 9: Quantum Theory and The Electronic Structure of Atoms

1
Module 9 Quantum Theory and The Electronic
Structure of Atoms

By Alyssa Jean-Mary
Source Modular Study Guide for First Semester
Chemistry by Anthony J. Papaps and Marta E.
Goicoechea-Pappas

2
Electromagnetic (EM) Radiation

Electronic transitions - associated with
absorption OR emission of electromagnetic
radiation, most of which cannot be seen, with
only the radiation that is in the visible region
of the electromagnetic spectrum being seen.

3
Electromagnetic (EM) Radiation Wave Nature

Wave nature of EM radiation
EM radiation travels in waves through space at
the speed of light (c), where c 3.00 x 108m/s
OR 3.00 x 1010cm/sec
Wave components
Crest top part of the wave
Trough bottom part of the wave
Wavelength (?) distance between peaks of
consecutive waves (i.e. distance from crest to
crest or trough to trough)
Units m, cm, OR Å (Angstrom), where 1 Å
10-10m 10-8 cm
Frequency (v) the number of waves that pass a
particular point in 1 second
Units Hertz (Hz) cycles/sec 1/sec sec-1
Wave equation v c / ?

4
Electromagnetic (EM) Radiation Particle Nature

Particle nature of EM radiation
Einstein discovered that the photoelectric
effect, which is when electrons are ejected from
the surface of a metal when light shines on it,
can be explained by postulating that light has
both wave and particle properties. When light is
a particle, it is known as a photon. Thus, since
light has both a wave nature and a particle
nature, it has what is called wave-particle
duality
Plancks Equation, which gives the energy of a
photon
E hv h (c / ?)
In this equation
E energy, with units of J (Joule) OR erg
(gcm2/sec2)
h Plancks constant 6.63 x 10-34 Jsec OR
6.63 x 10-27 ergsec
v frequency, with units of sec-1
c speed of light 3.00 x 108m/s OR 3.00 x
1010cm/sec
? wavelength, with units or m, cm, OR Å

5
Examples Using the Wave Equations

Example 1 If the wavelength of a light wave is
2335Å,
What is its frequency?
What is its energy in J?
What is its energy in erg?
Example 2 If the energy of a light wave is 6.66
x 10-20J,
What is its frequency?
What is its wavelength in cm?
What is its wavelength in Å?

6
Electromagnetic Spectrum

Electromagnetic spectrum different forms of
light arranged in a particular order according to
their energy, frequency, and wavelength
The visible region of the EM spectrum (violet to
red) 4000-7000 Å, OR 400-700 nm, OR 4.00 x
10-77.00 x 10-7 m

7
The Wave Nature of Electrons

L. de Broglie predicted that a particle that has
a mass (m) and a velocity (v) should have a
certain wavelength associated with it
? h / (mv), where h Plancks constant
This equation shows that wavelength and mass
wavelength and velocity are inversely
proportional to each other, so, if either the
mass or the velocity of a particle increases, its
wavelength decreases

8
An Example Using L. de Broglies Equation

Example 1 If a particle with a mass of 6.33 x
10-26 is travelling at 3.00 x 108 cm/sec, what is
its wavelength in cm?

9
The Bohr Atom, Quantization of Energy, Atomic
Spectra 1

Bohr Model of the atom assumes that electrons
revolve around the nucleus of an atom in circular
orbits
Quantization of energy When an atom is excited,
an electron is promoted from a lower energy level
(i.e. orbit) to a higher energy level (i.e.
orbit). This electron absorbs a definite (i.e.
quantized) amount of energy. When the electron
falls back to its original, lower energy level,
exactly the same amount of energy that it
absorbed by moving from the lower energy level to
the higher energy level is emitted.
This idea is illustrated in the picture below.
Here, n is the principal energy level or orbit.
As n increases, the energy levels or orbits get
closer to each other.
the maximum number of electrons per level max
e-/level 2n2
For n 1, max e- 2(1)2 2 for n 2, max e-
2(2)2 8 for n 3, max e- 2(3)2 18 for
n 4, max e- 2(4)2 32
The Bohr Model of the atom only predicts the
correct electronic structure for the first 18
elements.

10
The Bohr Atom, Quantization of Energy, Atomic
Spectra 2

Emission (i.e. bright line) spectra When the
electrons in an atom are exited to higher energy
levels by passing an electric current through a
gas in a vacuum tube at a very low pressure, the
light that the gas emits, which is due to the
electrons falling back to their original energy
levels, can be dispersed by a prism into distinct
lines. Each line corresponds to light with a
specific wavelength, frequency, and energy, an
thus, a specific color. The lines obtained are
referred to the emission spectrum of the element,
and each element has its own unique emission
spectrum.
In addition to using a prism to separate the
light into different wavelengths, a diffraction
grating can be used. In a diffraction grating,
the wavelengths that are the least energetic are
bent the most, which is opposite from a prism.

11
The Bohr Atom, Quantization of Energy, Atomic
Spectra 3

J. Balmer discovered that the wavelengths of
various lines in the hydrogen spectrum can be
related mathematically by the following empirical
equation
1 / ? (R)(Z2)((1/ni2) - (1/nO2))
Here, ? wavelength in m or cm R Rydberg
constant 1.097 x 107 m- 1.097 x 105 cm- Z
atomic number ni inner energy level no
outer energy level
This equation can only be used for any
hydrogen-like species (i.e. species that contain
only one electron (He, Li2, etc.)
1 / ? (R)(Z2)((1/ni2) - (1/nO2))
Here, ? wavelength in m or cm R Rydberg
constant 1.097 x 107 m- 1.097 x 105 cm- Z
atomic number ni inner energy level no
outer energy level

12
An Example Using the Bohr Atom, Quantization of
Energy, and Atomic Spectra

Example 1 Draw a diagram for the structure of
Aluminum-27 which indicates the number of
protons, neutrons, and electrons present, with
the electrons arranged in their principal energy
levels.
Example 2 If an electron in a sample of Li2
goes from energy level 3 to 1,
What is its wavelength in cm?
What is its wavelength in Å?
Is this transition in the visible portion of the
EM spectrum?
What is its frequency in sec-1?
What is its energy in J?
What is its energy in erg?

13
Quantum Mechanical Picture of the Atom

Bohr made significant contributions to the
understanding of atoms, including the still
unchallenged idea that the energy of an electron
in an atom is quantized, but, he did not give a
complete description of the electronic behavior
in atoms, such as the emission spectra of atoms
with more than one electron or the dual nature of
matter.
The Heisenberg Uncertainty Principle is one
important consequence of this dual nature matter.
It states that it is impossible to determine
accurately both the momentum, which is mass
multiplied by velocity, and the position of an
electron (or other very small particles)
simultaneously. To extend this principle, both
the energy and position of an electron cant be
known accurately at the same time. When this
principle is applied, it shows that electrons do
not orbit the nucleus in a well-defined path as
Bohr thought, because if they did, the position
of electrons could be more precisely determined
using the radius of the orbit as well as their
momentum (i.e. their kinetic energy) at the same
time.
Quantum mechanics is a highly mathematical branch
of chemistry/physics that treats small particles
as waves. It came out of a search to describe the
behavior of submicroscopic particles, since these
particles were found to not obey the laws of
classical mechanics. Using a complex mathematical
treatment, Schrödinger formulated an equation
that describes the behavior and energies of
submicroscopic particles. The Schrödinger
equation requires advanced calculus to solve.
This equation includes both the particle behavior
(in terms of mass) and the wave behavior (in
terms of a wave function that depends on the
location in space of the small particles) of
these small particles.

14
Quantum Mechanical Picture of the Atom Basic
Ideas of Quantum Mechanics

Atoms and molecules can exist only in certain
energy states. If an atom or molecule changes its
energy state, it will emit or absorb just enough
energy to bring it into the new energy state (the
quantum condition).
The energy lost, or gained, by an atom as it goes
from higher to lower, or lower to higher, energy
states is equal to the energy of the photon that
is emitted, or absorbed, during the transition.
Since a particle can behave as a wave, many of
the concepts and mathematical equations from wave
theory are used.
The allowed energy states, which are called
orbitals of atoms and molecules, can be described
by sets of four numbers, which are called quantum
numbers.
Since the exact energy of these orbitals can be
calculated, the exact position of the electron is
not known, a consequence of the Heisenberg
Uncertainty Principle.

15
Quantum Numbers (n, l, ml, ms)

There are 4 quantum numbers. These numbers
describe the electronic arrangement, or
electronic configuration, of atoms in space
Principal Quantum Number (n) main energy level
that an electron occupies
n is a positive integer (i.e. 1, 2, 3, 4, etc.),
and it represents shells in the Bohr atom (i.e. 1
K, 2 L, 3 M, 4 N, etc.)
Angular Momentum, Subsidiary, or Azimuthal
Quantum Number (l) specific kind of atomic
orbital (sublevel) that an electron occupies
l is a whole number (i.e. 0, 1, 2, 3, etc.), and
it is always 1 less than n. Also, it represents
different kinds of sublevels (i.e. 0 2, 1 p,
2 d, 3 f, etc.).
For example
if n 1, l can only 0, which corresponds to
sublevel s, so there is only one sublevel
(sublevel s) in the first energy level
If n 2, l can be 0 or 1, so it corresponds to
sublevels s and p, so there are two sublevels
(sublevels s and p) in the second energy level
Magnetic Quantum Number (ml) spatial
orientation of atomic orbitals i.e. how many
distinct regions of space (atomic orbitals) are
associated with a specific sublevel
ml is whole number that ranges from -l,0,l.
For example, if l 1, which corresponds to the
sublevel p, ml -1, 0, 1, which means there are
three distinct regions of space (atomic orbitals)
associated with the sublevel p
Electron Spin Quantum Number (ms) the spin of
an electron (either spin up or spin down) and the
orientation of the magnetic field produced by
this spin.
ms ½. This shows that each atomic orbital can
have only 2 electrons, one with ms ½ and the
other one with ms -½.
Pauli Exclusion Principle no two electrons in
an atom can have the same 4 quantum numbers

16
Permissible Values of the Quantum Numbers (n, l,
ml, ms) n 1 to 4
17
Examples Using Quantum Numbers

Are the following permissible or not permissible
sets of the four quantum numbers?
(0, 1, 1, -½)
(3, 2, -2, ½)

18
Orbital Diagrams Quantum Numbers 1

In orbital diagrams, orbitals are represented by
lines and electrons are represented by arrows,
with the orbitals being labeled using a number,
which represents the principal quantum number
(n), and a letter, which represents the
subsidiary quantum number (l).
See below for an example using 2p orbitals
The 2 represents n 2
Since n 2, l can be 1 or 0, but since it is p,
l 1
Since l 1, ml can be -1, 0, or 1, which means
there are three kinds of p orbitals, so there are
three lines, with, by convension, the first line
representing the most negative value of ml and
then decreasing the negative value until the last
line, which represents the least negative value
of ml
Since each orbital (i.e. line) can hold a maximum
of 2 electrons, two arrows are drawn on each
line, one facing up (ms 1/2) and one facing
down (ms -1/2)

19
Orbital Diagrams for n 1 to 4
20
Atomic Orbitals

An orbital is a region in which there is a high
probability of finding the electron. Remember
that each orbital in an atom can hold a maximum
of two electrons. If all of these atomic orbitals
are taken together, they appear as a diffuse
cloud of electrons.

21
Electronic Configuration

Electronic configuration electronic arrangement
(i.e. the arrangement of electrons) of an atom
Every electron in an atom has a position is space
that is defined by the principal energy
level/shell the sublevel/subshell or orbital
that it occupies
For example, 1s2, where
the number in front (1 in this case) represents
the principal energy level/shell, which is always
a whole number (i.e. 1, 2, 3, 4, 5, 6, or 7)
the letter (s in this case) represents the
sublevel/subshell or orbital, which can be s, p,
d, or f
the superscript number (2 in this case)
represents the number of electrons present in
this principal energy level/shell and
sublevel/subshell or orbital.
Each orbital can hold a maximum of 2 electrons
Since orbital s has 1 different type, it has a
max. of 2 x 1 2 electrons
Since orbital p has 3 different types, it has a
max. of 2 x 3 6 electrons
Since orbital d has 5 different types, it has a
max. of 2 x 5 10 electrons
Since orbital f has 7 different types, it has a
max. of 2 x 7 14 electrons

22
Electronic Configuration The Energies of
Orbitals 1

Aufbau Principle electrons will fill the lowest
energy atomic orbital available first
The below picture illustrates this order

23
Electronic Configuration The Energies of
Orbitals 2

The below picture gives the electronic
configuration, or electronic arrangement, of the
type of orbital occupied last

24
Electronic Configuration The Energies of
Orbitals 3

The larger the principle energy level, the
further away the electron is from the nucleus. If
electrons have the same principal quantum number,
their proximity to the nucleus follows the order
s, p, d, f, meaning that those in s are closest
to the nucleus, and those in f are further away
from the nucleus. The closer an electron is to
the nucleus, the less energy it has, and thus,
the harder it is to be removed from the atom.
For example, to remove a 3s electron from an
atom, more energy is needed, than to remove a 3p
electron.
Orbitals that have the same n and l, but
different ml and ms are degenerate, meaning that
they have the same amount of energy.

25
Electronic Configuration Writing Electronic
Configurations

To write electronic configurations, just follow
the periodic table, until the element is reached

26
Examples of Writing Electronic Configurations

Write the electronic configuration for each of
the following elements
Na
C

27
Electronic Configuration Writing Abbreviated
Electronic Configurations

When writing abbreviated electronic
configurations, the electronic configuration of
the noble gas (group VIIIA) previous to the
element is replaced by the symbol of the noble
gas enclosed in brackets. The rest of the
electronic configuration remains the same.

28
Examples of Writing Abbreviated Electronic
Configurations

Write the abbreviated electronic configuration
for each of the following elements
P
V

29
Electronic Configuration Orbital Diagram for the
Elements

Remember that in orbital diagrams, orbitals are
represented by lines and electrons are
represented by arrows, with the orbitals being
labeled using a number, which represents the
principal quantum number (n), and a letter, which
represents the subsidiary quantum number (l).
Since there is only 1 type of s orbital, it is
represented by 1 line
Since there are 3 types of p orbitals, they are
represented by 3 lines
Since there are 5 types of d orbital, they are
represented by 5 lines
Since there are 7 types of f orbitals, they are
represented by 7 lines
The following rules also need to be followed when
writing orbital diagrams
An orbital can have a maximum of 2 electrons,
with each electron having an opposite spin. This
is Paulis Exclusion Principle, which, stated
another way, is that no 2 electrons can have the
same set of 4 quantum numbers.
All orbitals of a given sublevel (i.e. degenerate
orbitals, orbitals with the same n and l) must be
occupied by a single electron, having the same
spin (spin up), before being paired.

30
Examples of Writing Orbital Diagrams

Write the orbital diagram for each of the
following elements
Si
Co

31
Electronic Configuration Exceptions to
Electronic Configurations and Orbital Diagrams

The elements in groups VIB (Cr, Mo, and W, but W
is actually not an exception to the rules) and IB
(Cu, Ag, and Au) of the periodic table dont
follow the rules given above.
Elements in VIB prefer to have sublevel d halfway
filled, so one of the two electrons in 4s is
taken to partially fill the last 3d orbital,
leaving the 4s orbital with only 1 electron (i.e.
partially filled).
Elements in IB prefer to have sublevel d
completely filled, so one of the two electrons in
4s is taken to completely fill the last 3d
orbital, leaving the 4s orbital with only 1
electron (i.e. partially filled).

32
Examples of Finding Electronic Configurations for
Elements with Exceptions to the Rules

Write the electronic configuration for each of
the following elements
Cr
Cu

33
Electronic Configuration Electronic
Configuration of Ions

To write the electronic configuration of an ion,
first write the electronic configuration for the
neutral atom. Then,
if the ion is negative (an anion), add as many
electrons to the last orbital(s) being filled as
the charge on the ion indicates.
if the ion is positive (a cation), remove as many
electrons from the least stable orbital(s) (i.e.
the orbital(s) with the highest energy the last
orbital(s)) as the charge on the ion indicates.
If the outermost electrons are in d orbitals,
electrons are removed from the s orbital first
and then from the d orbitals.
If the outermost electrons are in p orbitals,
electrons are removed from the p orbitals first,
then from the s orbital, and finally from the d
orbitals.