Download CHAPTER 4: ARRANGEMENT OF ELECTRONS IN ATOMS

The Development of a New
Atomic Model
The Rutherford model of the atom was
an improvement over previous models
of the atom.
 But, there was one major problem:
 If the electrons are negatively charged
and the nucleus was positively charged,
then what prevented the electrons from
being drawn into the nucleus?

Properties of Light
Prior to 1900, most scientists believed
that light behaved as waves.
 We later found that light also behaves
as particles, but most of light’s
properties can be attributed to its wavelike behavior.

Electromagnetic Radiation
What is electromagnetic radiation
(EMR)?
 Answer: a form of energy that exhibits
wavelike behavior as it travels through
space
 Examples of EMR include X rays, UV
light, microwaves, visible light and radio
waves.

Electromagnetic Radiation
(cont’d)
When all forms of EMR are brought
together, the electromagnetic spectrum
is formed.
 All forms of EMR travel at the same
speed through a vacuum at 3 x 108 m/s.

Electromagnetic Spectrum
Light as Waves
Light is repetitive in nature similar to
waves.
 Some of the most measurable
properties of waves are wavelength and
frequency.
 Wavelength () is the distance between
corresponding points on adjacent
waves.

Light as Waves (cont’d)
Wavelength can be measured in meters,
centimeters, or nanometers.
 The primary choice for wavelength is
nanometers ( 1nm = 1 x 10-9 m).
 Frequency () is defined as the number
of waves that pass a given point in a
specific time, usually one second.
 Frequency is measured in hertz (Hz).
 1 hertz = 1 wave/second

Light as Waves (cont’d)
Light as Waves (cont’d)

We can write a mathematical expression that
relates frequency and wavelength.

c = 
In the previous equation, c is the speed of
light,  is the wavelength, and  is the
frequency.
Since the speed of light is the same for all
forms of EMR, the product of wavelength and
frequency is constant. Therefore, wavelength
and frequency are inversely proportional.


The Photoelectric Effect
Scientists conducted an experiment
involving the interactions between light
and matter that could not be explained
by the wave theory.
 This experiment revolved around the
idea of the photoelectric effect.
 Photoelectric effect refers to the
emission of electrons from a metal when
light shines on the metal.

The Photoelectric Effect (cont’d)
The remaining question surrounding the
photoelectric effect dealt with frequency
of light that struck the metal.
 During the course of the experiment, no
electrons were emitted if the frequency
was below a certain minimum.
 According to the wave theory of light,
any frequency of light should have
knocked loose an electron.

The Photoelectric Effect (cont’d)
Light as Particles
In 1900, German physicist Max Planck
begins to explain the photoelectric
effect.
 His explanation was based on the
emission of light by hot objects.
 He proposed that hot objects did not
continuously emit EMR, instead the
released small, specific amounts of
energy called quanta.

Light as Particles (cont’d)
A quantum is the minimum amount of
energy that can be gained or lost by an
atom.
 Planck derived a relationship between a
quantum and the frequency of radiation.

E = h
 E = energy (in joules),  = frequency,
and h = Planck’s constant
 h = 6.626 x 10-34 Js

Light as Particles (cont’d)
In 1905, Albert Einstein expands on
Planck’s idea about quanta.
 Einstein proposes that EMR has a
wave-particle duality.
 Since light and other forms of EMR can
be thought of as waves, then EMR can
also be thought of as a stream of
particles. These particles are called
photons

Light as Particles (cont’d)
Photons are particles of EMR that have
zero rest mass and a quantum of energy.
 We can rewrite the relationship between
energy and frequency in terms of photons.

Ephoton = h
 From this equation, Einstein concluded that
in order for an electron to be ejected from
the metal, it must be struck by one photon
that has at least the minimum energy
required.

Light as Particles (cont’d)
So, the minimum amount of energy
needed is tied to the minimum frequency
of the light needed.
 Different elements required different
minimum frequencies to undergo the
photoelectric effect.
 Einstein eventually wins Nobel Prize for
Physics in 1924 due to this work.

The Hydrogen-Atom LineEmission Spectrum
Electrons can gain or lose energy as we
have previously discussed.
 Electrons can be in the ground state or
the excited state.
 The ground state is the lowest energy
state for an atom and it is the most
stable.
 The excited state is any state in which
the atom has a higher potential energy
than the electron’s ground state.

Hydrogen-Atom Line-Emission
Spectrum (cont’d)
When scientists passed electric current
through a vacuum containing hydrogen
gas at low pressure, the excited
hydrogen atoms had a pinkish glow.
 When this light was passed through a
prism, it split into specific color bands.
 This is called the line-emission spectrum
of hydrogen.

Hydrogen-Atom Line-Emission
Spectrum (cont’d)
Hydrogen-Atom Line-Emission
Spectrum (cont’d)
Ground State vs. Excited State
In order to an atom (or electron) to get to
the excited state from the ground state,
energy has to be added.
 Once an atom (or electron) reaches the
excited state and begins to return to the
ground state or to a lower energy state, the
atom releases a photon of energy.
 This photon has an energy that is
equivalent to difference between the two
energy states.
 Ephoton = E2 – E1 or Ei - Ef

Ground State vs. Excited State
(cont’d)
Bohr Model of the Hydrogen
Atom
1913- Danish physicist Niels Bohr
proposed an atomic model based on
electrons and photon emission.
 The Bohr model suggests that electrons
circle the nucleus in circular paths called
orbits.
 The atom and electrons are in the
lowest energy state (ground state) when
the electrons are in orbits closest to the
nucleus.

Bohr Model of the Hydrogen
Atom (cont’d)
The energy of the electron increases
when the orbits are farther from the
nucleus.
 In order for electrons to move to another
orbit, a photon of energy must be
absorbed by the electron. This energy
must equal the energy difference
between the two orbits. (See the
formula discussed during ground state
vs. excited state)

Bohr Model of the Hydrogen
Atom (cont’d)

In order for an electron to move from an
state of higher energy to one of a lower
energy, it must release a photon of
energy equal to the difference between
the two energy levels.
Representation of Bohr Model
The Quantum Model of the Atom
Electrons as Waves
 1924- French scientist Louis de Broglie
asks, “Could electrons have a dual
wave-particle nature as well?”
 De Broglie suggested that electrons be
considered as waves confined to the
space around an atomic nucleus.

The Quantum Model of the Atom
(cont’d)
The Heisenberg Uncertainty Principle
(HUP)
 1927- German theoretical physicist
Werner Heisenberg decided to attempt
to detect electrons by using their
interactions with photons.
 Since photon have about the same
energy as electrons, finding a specific
electron with a photon would knock the
electron off course.

The Quantum Model of the Atom
(cont’d)
Because of this, there is always an
uncertainty in attempting to find an
electron.
 HUP: It is impossible to know both the
position and velocity of an electron.

The Quantum Model of the Atom
(cont’d)
The Schrodinger Wave Equation (SWE)
 1926- Austrian physicist Erwin
Schrodinger uses the wave-particle
duality to write an equation that treats
electrons as waves.
 Pairing the SWE and the HUP together
led to the foundation of modern quantum
theory.

The Quantum Model of the Atom
(cont’d)
When the SWE is solved, the results are
wave functions.
 Wave functions can only give the
probability of finding an electron at a given
point.
 Due to wave functions, we know that
electrons do not travel in circular orbits.
Instead, electrons reside in certain regions
called orbitals (3-D regions about the
nucleus that indicates the probable location
of an electron).
