Transcript n - Valdosta State University

Atomic Structure
Chapter 7:
1. Describe the properties of electromagnetic
radiation.
2. Understand the origin of light from excited atoms
and its relationship to atomic structure.
3. Describe the experimental evidence for waveparticle duality.
4. Describe the basic ideas of quantum mechanics.
5. Define the three quantum numbers and their
relationship to atomic structure.
Electromagnetic Radiation
• Radiation is _____________!
• List forms of electromagnetic radiation:
_______________
___________
_______________
___________
• Maxwell Theory (1831-1879): describe all
forms of radiation in terms of ________
________________________________.
• Einstein Theory (1879-1955): light has
_______________________________.
Wave Properties
Visible light
Ultraviolet
radiation
wavelength
Electromagnetic Radiation
Frequency – hertz (s-1)
Speed = wavelength (m) x frequency (s-1)
c = lx v
What is the frequency of orange light,
which has a wavelength of 625 nm?
Students should be familiar with conversion of
units and conversion between l and v.
The Visible Spectrum of Light
• Long wavelength --> ______ frequency
_____ energy
• Short wavelength --> _____ frequency
_____ energy
Energy and Frequency
• Max Planck (1858-1947): the energy of
a vibrating systems is proportional to
the frequency of vibration.
• The proportionality constant
h = Planck’s constant
= 6.6260693 x 10-34 J s
E=hv
Radiation given off by a Heated Body
• Planck solved the
“___________________”.
• Vibrations are _________
– only vibrations with
specific frequencies are
allowed.
• There is a distribution of
vibrations in a object.
Quantization of Energy
• An object can gain or lose energy by
absorbing or emitting radiant energy in
QUANTA.
• Energy of radiation is proportional to
frequency.
Light with large l (small v) has a _____ E.
Light with a short l (large v) has a ____ E.
E = h v
Photoelectric Effect
• Experiment demonstrates the _______
_____________________________.
No e- observed until
light of a certain
minimum E is used.
Photoelectric Effect
• Classical theory said that E of ejected
electron should increase with increase
in light frequency—not observed!
• No e- observed until light of a certain
minimum E is used.
• If the frequency is above the minimum,
the number of e- ejected depends on
light intensity.
• Einstein explained the photoelectric effect:
light consists of “__________” particles
called PHOTONS – _______________.
• The energy of each photon is proportional to the
______________of radiation (Planck’s relation).
• The greater the intensity of light, the more photons
are available to strike per unit of time.
Show that the energy of a mol of blue photons (l = 400
nm) is higher than the energy of a mol of red photons
(l=685 nm)
Using Planck’s Equation
v = c/l
E=hv
~
E=hv=hc =hcv
l
(wavenumber)
• As frequency (v) increases, energy (E) __________.
• As wavelength (l) decreases, energy (E) _________.
Students should be familiar with frequency,
wavelength, and energy calculations.
What is the color of light when its
frequency is 6.0 x 1014 s-1?
Photosynthesis
• Chlorophylls absorb blue and red light and carotenoids absorb
blue-green light, but green and yellow light are not effectively
absorbed by photosynthetic pigments in plants; therefore, light
of these colors is either reflected by leaves or passes through
the leaves. This is why plants are green.
Spectrum of White Light
Spectrum of Excited Hydrogen Gas
• Excited atoms emit light of only certain wavelengths.
–Evidence of ____________________.
• Line Emission Spectra of Excited Atoms.
• The wavelengths of emitted light depend on
______________________________.
Which Mathematical Expression represents the
Regular Patterns of Emission?
• Johann Balmer (18251898) and Johannes
Rydberg (1854-1919)
developed an equation:
• Rydberg equation – to
calculate the
_________________
__________________
__________________.
• Rydberg constant = R
R = 1.0974 x 107 m-1
1
=R
l
(
1
22
1
)
2
n
when n > 2
n = 3 , l =red line
n = 4 , l = green line,
Etc.
Balmer Series
Atomic View of the Early 20th
Century
An electron (e-)
traveled about the
nucleus in an orbit.
1. Any orbit should be
possible and so is any
energy.
2. But a charged particle
moving in an electric
field should emit
energy.
End result should be
matter selfdestruction!
Bohr Model
• Niels Bohr (1885-1962) connected the
observation of the spectra of excited atoms
with the quantum ideas of Planck and Einstein.
• Based on Rutherford’s work – electrons are
arranged in space outside the atom.
• Bohr model shows electrons moving in a
circular orbit around the nucleus.
• Bohr postulated:
1.- An electron could occupy only __________
___________or energy levels in which it is
stable.
2.-The energy of the electron in the atom is
______________.
Atomic Spectra and Bohr
Potential energy of electron = En = - R h c
n2
in the nth level
• n  ___________ quantum number
• n is a _________________ having values of 1, 2, 3
and so on.
• The energy of attraction between oppositely
charged bodies (negative electron and positive
nuclear proton) has a negative value. The value
becomes more negative as the bodies move closer
together (Coulomb’s law).
• As the value of n increases, the energy becomes less
negative, the distance of the electron from the
nucleus increases.
Atomic Spectra and Bohr
• Only orbits where n = integral
number are permitted.
If e-’s are in quantized energy
states, then ∆E of states can
have only certain values. This
explain sharp line spectra.
E = -C (1/ 2
E = -C (1/1
2 )
2 )
n=2
n=1
Ground State and Excited State
• Ground state: The state of an atom in which all
electrons are in the ______________________.
• Excited state: The state of an atom in which at
least one electron is ______________________
____________________.
CC alculate DE for an e- of the H atom “falling”
from high energy level (n = 2) to low energy level (n
= 1).
Atomic Spectra and Bohr
• The amount of energy that must be absorbed by the atom so
that an electron can move from the first to the second energy
state is 3/4RhC or 984 kJ/mol of atoms – no more or less –
energy levels in the H atom are quantized – only certain
amounts of energy may be absorbed or emitted.
• When an electron “falls” from a level of higher n to one of
lower n, ________ energy. The negative sign indicates energy
is _________, 984 kJ must be _______ per mole of H atoms.
• The energy ________ is observed as ______ – This is the
source of the lines observed in the emission spectrum of H
atoms. – The basic explanation holds for the spectra of other
elements.
Atomic Spectra and Bohr
∆E = Efinal – Einitial = -R h c
1
( n2
final
-
1
n2initial
)
• The origin of atomic spectra is the movement
of _________ between quantized energy
states.
• Electron is excited from a lower energy state
to a higher one – Energy is ________.
• Electron moves from a higher energy state to
a lower one – Energy is _________.
Electronic Transitions in an
Excited H Atom
• If electrons move from
energy states n >1 to the
n =1 state – emission lines
have energies in the UV
region (Lyman series).
• If electrons move from
energy states n >2 to the
n =2 state – emission
lines have energies in the
VIS region (Balmer
series).
• If electrons move from
energy states n >3 to the
n =3 state – emission
lines have energies in the
IR region.
Calculate the wavelength of the photon emitted if
an electron in the H atom moves from n = 4 to n =2
Flaws in Bohr’s Theory
• Bohr’s model of the atom explained only
the spectrum of H atoms and of other
systems having one electron (such as
He+).
• The idea that electrons are particles
moving about the nucleus with a path of
fixed radius, like that of the planets
about the sun, is no longer valid.
Wave Mechanics
Louis de Broglie (1892-1987)
proposed that all moving
objects have _______
_________________(1924).
For light: (1) E = mc2
(2) E = h v = h c / l
Wave Mechanics –
Calculate the Broglie Wavelength
l=h
mv
Baseball (115 g) at 100 mph
e- with velocity = 1.9 x 108 cm/sec
It is possible to observe wave-like properties
only for particles of extremely __________,
such as protons, neutrons, and electrons.
The Uncertainty Principle
• Erwin Schrödinger, 1887-1961 : developed
________________or ______________.
• Werner Heisenberg, 1901-1976 : The
uncertainty principle – it is impossible to fix
both the ______________ electron in an atom
and its ________ with any degree of certainty.
• Max Born, 1882-1970 : if the energy of an
electron in an atom is known with a small
uncertainty, there will be large uncertainty in
its position in the space about the atom's
nucleus.
• We can assess only the likelihood, or
probability, of finding an electron with a given
energy within a given region of space.
Schrödinger's Wave Functions
1.
The behavior of the electron
in the atom is best
described as a standing wave
– In a vibrating string, only
certain vibrations can be
observed = only certain wave
functions are allowed for the
electron in the atom.
2. Each wave function () is
associated with an allowed
energy value, En, for the
Wave motion:
electron.
wave length and nodes
3. Then, from 1 and 2, the
energy of the electron is
4. In contrast to Bohr’s
quantized – only certain
theory – quantization is
values of energy.
imposed as a postulate.
Schrödinger's Wave Functions
5. The is related to the probability of finding
the electron within a given region of space =
_______________.
6. Energy is known precisely – position is given
by a probability. The region of space in which
an electron of a given energy is most probably
located is called its _______________.
7. The solution to the Schrödinger's equation,
for an electron, in a 3-D space, are 3 integer
numbers = quantum numbers n, l, and ml.
These numbers have only certain combination
of values.
Quantum numbers
• n, Principal quantum number = 1, 2, 3, …
Determines the ________ of the electron. Also related to size of
orbital.
En = - Z2h R / n2
Electrons with the same n value are in the same electron ______ or
same electron _________.
• l, Angular Momentum quantum number = 0, 1, 2, 3, …, n-1
Determines the ______ at which electrons circulate about the nucleus.
Related to orbital __________.
Electrons with the same l value are in the same _______ and have
the same orbital _____ (______). All orbitals in the same subshell
have the same ___________.
• ml, Magnetic quantum number = 0, ±1, ± 2, ± 3, …, ±l
Determines the _____________ of the orbital motion of the electron.
(Clockwise or counterclockwise). Related to ___________ in space
of the orbitals within a subshell, this gives the ___________ of
orbitals in a subshell.
See Table 7.1 (p 319)
Quantum numbers and Orbitals
Number of subshells in a shell = n
Number of orbitals in a subshell = 2l + 1
Number of orbitals in a shell = n2
l =0 (s) ; l =1 (p) ; l =2 (d) ; l =3 (f)
Name of orbital = value of n and letter code for l
If n=1 ; l = n-1 = 0 ; ml = 0
Only 1 subshell (s); only 1 orbital (1s)
If n=2 ; l = 0, 1 ; ml = +1, 0, -1
There are 2 subshells (s and p)
4 orbitals (the 2s, and three 2p (3 orientations)
Orbitals
• Electron orbitals are probabilities –
represented as ____________________.
Orbitals
surface density plot
or radial distribution plot
• For the s orbital, the probability of finding an
electron is the same at the same distance from the
nucleus – the 1s orbital is ____________ in shape.
• Quantum mechanics – electron has wave properties –
the maximum amplitude of the electron wave occurs
at 0.053 nm from the nucleus.
• Bohr’s radius = 0.059 nm
Orbitals
• The p orbitals have 1 nodal surface – zero probability of
finding an electron.
• Number of nodal surfaces = value of l
• There are three p orbitals in each p subshell: ml = +1, 0, -1
• Refer to orbitals according to the axes along which the
lobes lie: px, py, pz
Orbitals
• The d five orbitals, l=2 have
2 nodal surfaces (may not
be flat).
• What type of orbital is
designated n = 4, l = 3, ml =-3?
a. 4s
b. 4p
c. 4d
d. 4f
e. none
Orbitals
Students should be familiar with definitions
of quantum numbers and orbital types.
Practice
•
Which of the following represent valid sets
of quantum numbers?
a) n=3, l=3, ml= +1
b) n=5, l=1
c) n=6, l=5, ml=1
d) n=4, l=3, ml=-4
Remember
• Go over all the contents of your
textbook.
• Practice with examples and with
problems at the end of the chapter.
• Practice with OWL tutors.
• W ork on your assignment for Chapter
7.
• Practice with the quiz on the cd or
online service.