Download Chapter 5: Electrons in Atoms 1 Section 5.1: Light and Quantized

Chapter 5: Electrons in Atoms 1
Section 5.1: Light and Quantized Energy
Rutherford proposed that all of an atom’s positive
charge and most of its mass are concentrated in
the nucleus, surrounded by fast-moving electrons.




major scientific development, but incomplete
lacks detail about how electrons occupy
space around the nucleus
doesn’t explain why the negatively charged
electrons are not pulled into the positivelycharged nucleus
doesn’t account for differences in chemical
behavior among elements
Wave nature of light
Electromagnetic radiation: form of energy that
exhibits wavelike behavior as it travels through
space.
 radio waves
All EM waves travel at
 microwave
3.0 x 108 m/s in a
 infrared
vacuum, represented by
 visible light
“c”
 ultraviolet
 x-rays
 gamma
Early 1900s, scientists observed certain elements
emit visible light when heated in a flame.







Chemical behavior is related to the
arrangement of the electrons in the atoms
Wavelength, represented by λ (lambda)
Frequency, represented by ν (nu) = number of
waves that pass a given point each second
o measured in hertz (Hz) = 1 wave/s
o Hz = 1/s (where wave is understood) or s-1
o Ex. 652 Hz = 652 waves/s = 652/s or 652 s-1
Amplitude: wave’s height from origin (or
resting point) to crest or from origin to trough
speed of light = wavelength x frequency
c=λν
Speed of all waves is the same, but may have
different wavelengths and frequencies
Wavelength and frequency are inversely
related
Sunlight is called white light – contains a continuous
range of wavelengths and frequencies
 Passing through a prism separates the light into
a spectrum of colors
 Short wavelengths bend more than long
wavelengths
 ROY G BIV – colors of the spectrum
 Red – longer wavelength, less energy
Violet – shorter wavelength, more energy
 Use c=λν to calculate wavelength or frequency
of any wave.
crest
amplitude
wavelength (λ)
trough
Visible light:
red has longer wavelengths, lower frequency
violet has shorter wavelengths, higher frequency
Sample problem
What is the wavelength (λ) of a microwave with a
frequency of 3.44 x 109 Hz?
c = λν c = λ
v
λ = 3.0 x 108 m/s
3.44 x 109 s-1
λ = 8.72 x 10-2m Practice problems: p. 121, #s 1-4
Chapter 5: Electrons in Atoms 2
Particle Nature of Light
Aspects of light NOT explained by wave model:
1. Why heated objects emit only certain frequencies
of light at a specific temperature.
2. Why some metals emit electrons when colored
light of a specific frequency shines on them.
a. Ex: iron at room temp is a dark gray
iron when heated, glows red
when heated further, glows blue
Mathematically, energy of a quanta is related to
the frequency (ν) of the emitted radiation.
Energy = Planck’s constant x frequency
E = hν
h = Planck’s constant = 6.626 x 10-34 Js
J = Joule (SI unit of energy)
Energy increases as frequency increases.
1900, German physicist Max Planck studied light
emitted from heated objects.
 Matter can gain or lose energy only in small,
specific amounts called quanta.
 Quantum: minimum amount of energy that can
be gained or lost by an atom
Ex. Heating a cup of water in a microwave:
 temperature appears to rise in a
continuous manner
 Actual temp increases in small,
infinitesimal steps as its molecules absorb
quanta of energy
 Because steps are small, it appears
continuous rather than stepwise.
Planck’s theory: for a given frequency (ν),
matter can emit or absorb energy only in whole
number multiples of hv (1 hv, 2 hv, 3 hv, etc.)
 Matter can only have certain amounts of
energy
 Quantities of energy between these
values don’t exist
1905 – Albert Einstein proposed the electromagnetic
radiation has both wavelike and particle-like natures
Sample problem:
What is the energy of a photon from the violet
portion of the rainbow if it has a frequency of
7.23 x 1014 s-1?
Photon: particle of EM radiation with no mass that
carries a quantum of energy
 A photon’s energy depends on its frequency
 Ephoton = hν
 Energy of a photon of light must have a certain
minimum value (threshold) to cause the
ejection of a photoelectron
o For photoelectric effect to occur, the
photon must have the minimum
amount of energy required to free an
electron from the atoms of the metal.
Atomic Emission Spectra
How neon lights work:
pass electricity through a tube filled with neon gas
 Neon atoms absorb energy, become excited
 Pass the light emitted by neon atoms through
a prism, and neon’s atomic emission spectrum
is produced
Atomic emission spectrum of an element: set of
frequencies of EM waves emitted by atoms of an
element
Photoelectric effect: electrons (called
photoelectrons) are emitted from a metal’s
surface when light of a certain frequency shines
on the surface.
Ex. Solar calculator: photoelectric cells convert
incident sunlight into electrical energy .
Ephoton = hv
Ephoton = (6.626 X 10-34 Js)(7.23 x 1014 s-1)
Ephoton =4.79 x 10-19 J
Practice problems: p. 124, #s 5-6
Neon has several individual lines of color – it’s
not continuous.
Each element’s atomic emission spectrum is
unique.
 Can be used to identify that element
 Can determine the composition of an
unknown compound.
Behavior of light can only be explained by the dual
wave-particle model!
Chapter 5: Electrons in Atoms 3
Section 5.2: Quantum Theory and the Atom
Niels Bohr worked in Rutherford’s lab
DeBroglie’s Wave-Particle Duality
1913 – proposed the following while working with
hydrogen (why hydrogen’s emission spectra was not
continuous)
1924, Louis de Broglie proposed an idea that
eventually accounted for the fixed energy levels
of Bohr’s models
 Bohr’s quantized electron orbits had
characteristics similar to waves
o If waves can have particle-like
behavior, can particles like electrons
behave like waves?
o If an electron has wavelike motion and
is restricted to circular orbits of fixed
radii (plural of radius), then the
electron is allowed certain
wavelengths, frequencies, and
energies.
 DeBroglie developed an equation relating
wavelength (λ) of a particle with mass (m)
moving at a velocity (v)

Atoms have only a finite number of energy states
o Ground State – lowest possible energy state
o Excited State – any other energy state
o The more energy in an atom, the larger its orbits
(the farther the electrons orbit away from the
nucleus)
o When an electron is in a higher energy orbit, it can
move to a lower orbit by emitting a photon of
equal energy to the difference between the
energy levels
∆E = Ehigher-energy orbit ― Elower-energy orbit = Ephoton = hν
o
o
Since electrons must move between well defined orbits, only certain frequencies of EM
radiation can be emitted
The emitted frequencies of light produce the
emission spectrum of that element
Bohr’s model works well for hydrogen, but not for the
other elements.


Bohr’s model is not widely accepted or currently used.
Bohr’s model did provide the basis for quantum
theory
Errors in Bohr’s Models
1. Energy levels are similar to planetary orbits (circular)
2. Energy levels are equally spaced (like rungs on a
ladder).
Practical application of DeBroglie’s Wave-Particle Duality
 Wave – pencil in water appears bent or broken –
automatic doors
 Particle – solar power
Heisenberg’s Uncertainty Principle
It is impossible to know both the exact position and
velocity of a particle at the same time.

λ=h
or
λ=h
mv
p
DeBroglie’s equation predicts that all
moving particles (like electrons) have wave
characteristics.
o proven by subsequent experiments
o wave-like behavior and particlelike behavior of electrons cannot
be observed at the same time
DeBroglie’s Wave-Particle Duality explains
radioactive decay:
 Alpha has both particle and wave properties
o Particle properties do not provide
enough energy to overcome nuclear
attraction
o Wave properties allow for existence
outside the nucleus
Schrodinger’s Wave Equation
Furthered de Broglie’s wave-particle theory
 Equation treated hydrogen’s electron as a wave
o Worked for other elements, also
(Bohr’s model didn’t)
 Atomic model where electrons are treated as
waves = wave mechanical model or the
quantum mechanical model
Chapter 5: Electrons in Atoms 4
Quantum mechanical model:
Quantum Theory


Key concept of Schrödinger's Equation is
quantum numbers
1. Quantum numbers represent different
energy states of electrons
2. Changes take place by absorbing/releasing
photons
3. Electrons can occupy the same energy level
without affecting each other

Limits an electron’s energy to certain values
Doesn’t describe the electron’s path around the
nucleus
The solution to Schrödinger’s wave equation is
known as a wave function
o wave function is related to the
probability of finding the electrons in a
particular volume of space around the
nucleus
o electrons are more likely in certain areas
accounting for the shape of orbitals
o atomic orbital: a 3-dimensional region
around the nucleus that describes the
electron’s probable location (fuzzy cloud)
Energy Sublevels and Orbitals
Sublevels – divisions within each of the principal
energy levels
 Principal energy level 1 has 1 sublevel, level 2
has 2 sublevels, etc.
o Number of sublevels is equal to the
principal quantum number (n) of that
level
 Sublevels are identified by the letters s, p, d, f
o Beginning with level 4, sublevels will
overlap
o Letters are based on the original
spectroscopy lines:
 s = sharp
 p = principal
 d = diffuse
 f = fundamental
Each pair of electrons occupies an orbital:
s=1
p=3
d=5
f=7
Maximum number of electrons in a sublevel:
s = 2 p = 6 d = 10 f = 14
(each orbital can contain up to 2 electrons)
Sublevels are preceded by the principal quantum
number (for example: 1s, 3p, …
Ex. Principal level 2 consists of 2s
and 2p, level 3 consists of 3 sublevels:
3s, 3p, and 3d, level 4 consists of …
Principal quantum numbers (n):





Indicate the relative sizes and energies of
atomic orbitals
As n increases, the orbital becomes larger and
the electron spends more time farther from
the nucleus and the energy level increases
Lowest principal energy level is assigned a
principal quantum number of 1 (n = 1,
electron is in its ground state)
o n goes up to 7
Corresponds to the period number on the
periodic table
Greatest number of electrons that may
occupy any level is 2n2.
Hydrogen’s First Four Principal Energy Levels
Principal
quantum
number (n)
Sublevels
(types of
orbitals)
present
Number of
orbitals
related to
sublevel
1
2
s
s
p
s
p
d
s
p
d
f
1
1
3
1
3
5
1
3
5
7
3
4
Total
number of
orbitals
related to
principal
energy level
2
(n )
1
4
9
16
Chapter 5: Electrons in Atoms 5
Shape of the electron cloud



Larger the principal quantum number (n), the
larger the cloud
Size is also determined by attraction of the
nucleus and the repulsions of the other
electrons
All clouds in a level, when combined, will
form a sphere
Within the principal levels, orbitals can have
different spatial orientations (m) (directions):
 p sublevel had 3 possible values (x, y, z
oriented along the 3 coordinate axes)
 d sublevel has 5 possible values
 f sublevel has 7 possible values
At any given time, an electron can occupy just one
orbital.
Hydrogen’s 1 electron in the ground state
occupies the 1s orbital. If it gains a quantum of
energy, it can move to the 2s orbital, to one of
the 3p orbitals, or to another vacant orbital.
Degenerate orbitals – orbitals of the same size
and shape but different spatial orientation
Section 5.3: Electron Configurations
The arrangement of electrons follows a few very specific
rules (with the occasional exception!)
Electron configuration: the arrangement of electrons in
an atom
 low-energy systems are more stable than highenergy systems
 electrons tend to arrange themselves in the
lowest possible energy system
 ground-state electron configuration
3 rules (principles) define how electrons can be
arranged in an atom’s orbitals.
The aufbau principle: each electron occupies
the lowest energy orbital available
 learn the sequence of atomic orbitals
from lowest energy to highest energy
In the diagram at left (textbook page 135),
each box represents an atomic orbital.




All orbitals related to an energy
sublevel have equal energy (ex. all
three 2p orbitals have equal energy)
Energy sublevels within a principal
energy level have different energies
(ex. three 2 p orbitals have higher
energy than the 2s orbital)
o energy increases as the level
changes
In order of increasing energy:
s, p, d, f
Orbitals can overlap (ex. 4s has lower
energy than 3d and will fill in first)
Chapter 5: Electrons in Atoms 6
Each electron in an atom has a spin (like a top on its
axis)
 The electron can only spin in 2 possible
directions (↑↓)
The Pauli exclusion principle:

Only 2 electrons can occupy a single atomic orbital
o electrons must have opposite spins
Hund’s rule: single electrons with the same spin must
occupy each equal-energy orbit before other electrons
with opposite spins can occupy the same orbital
 Ex. One electron enters each of the three 2p
orbitals before a second electron can enter any
of the orbitals.
Orbital diagrams and electron configuration notations: 2 methods for representing an atom’s electron configuration
Method 1
Orbital diagram: includes a box for each of the atom’s orbitals. An empty box
box containing a single up arrow
down arrows
↑↓
↑
is an unoccupied orbital. A
represents an orbital with 1 electron. A box containing both up and
represents a filled orbital. Each box is labeled with the principal quantum number and
sublevel associated with the orbital.
The number of electrons
equals the number of
protons, which is represented
by the atomic number.
Example: Carbon
Atoms are not actually built
electron by electron.
Method 2: Electron configuration notation






Designates the principal energy level and energy sublevel associated with each orbital
Includes a superscript representing the number of electrons in the orbital
Carbon looks like this:
1s22s22p2.
See textbook, pg. 137, table 5-3
See page 138 for order of filling sublevels (next page of notes)
What is the electron configuration notation for oxygen?
Method 2b: Noble-gas configuration
 Helium: 1s2. *He+ also represents helium’s electron configuration
 Neon: 1s22s22p6. [Ne]
 Sodium is the first element in the 3rd principal level. Its configuration can be written as 1s22s22p63s1. Or, since
sodium has the same electron configuration for its innermost electrons as neon, sodium can be written as
[Ne]3s1.
 What is the electron configuration for magnesium?
Chapter 5: Electrons in Atoms 7
Valence electrons:


electrons in the atom’s outermost orbitals, generally
those in the highest principal energy level
electrons that are involved in the formation of chemical
bonds
Electron-dot structures:


consists of the element’s symbol, representing both the
element’s nucleus and its inner-level electrons
surrounded by dots representing the atom’s valence
electrons
o dots are placed one at a time
 pair the s-level electrons first
 fill all remaining p-orbitals (one dot on
each of the other 3 sides) before pairing
up remaining electrons (see below)