Transcript Chapter 7-part 1

Chapter 7
The Quantum-Mechanical Model
of the Atom
A Theory that Explains Electron Behavior


the quantum-mechanical model explains the manner electrons exist
and behave in atoms
helps us understand and predict the properties of atoms that are directly
related to the behavior of the electrons
◦ why some elements are metals while others are nonmetals
◦ why some elements gain 1 electron when forming an anion, while
others gain 2
◦ why some elements are very reactive while others are practically inert
◦ and other Periodic patterns we see in the properties of the elements
2






One of the ways that energy travels through space:
– Light from sun; microwave oven; radiowaves for MRI mapping
• Exhibit the same type of wavelike behavior and
travel at the speed of light in a vacuum
• It has electric and magnetic fields that
simultaneously oscillate in planes mutually
perpendicular to each other and to the direction
of propagation through space.
Electromagnetic radiation has
oscillating electric (E) and magnetic
(H) fields in planes
The Nature of Light its Wave Nature


light is a form of electromagnetic radiation
◦ composed of perpendicular oscillating waves, one for the electric field
and one for the magnetic field
 an electric field is a region where an electrically charged particle
experiences a force
 a magnetic field is a region where an magnetized particle experiences a
force
all electromagnetic waves move through space at the same, constant speed
◦ 3.00 x 108 m/s in a vacuum = the speed of light, c
4
Characterizing Waves

Waves are characterized by wavelength, frequency, and speed.
– wavelength (λ) is the distance between two

consecutive peaks or troughs in a wave.
– frequency (ν) is defined as the number of waves (cycles) per second
- is a measure of the distance covered by the wave
◦ the distance from one crest to the next

◦ the number of waves = number of cycles
◦ units are hertz, (Hz) or cycles/s = s-1
 1 Hz = 1 s-1

the amplitude is the height of the waVe
◦ the distance from node to crest
 or node to trough
◦ the amplitude is a measure of how intense the light is – the larger
the amplitude, the brighter the light
5
Amplitude & Wavelength
Dim light
Bright light
6
Interference


the interaction between waves is
called interference
when waves interact so that they
add to make a larger wave it is
called constructive interference
◦ waves are in-phase

when waves interact so they
cancel each other it is called
destructive interference
◦ waves are out-of-phase
7
Diffraction



when traveling waves encounter an obstacle or opening in a barrier that
is about the same size as the wavelength, they bend around it – this is
called diffraction
◦ traveling particles do not diffract
the diffraction of light through two slits separated by a distance
comparable to the wavelength results in an interference pattern of the
diffracted waves
an interference pattern is a characteristic of all light waves
8
2-Slit Interference
9
The Relationship Between Wavelength
and Frequency


for waves traveling at the same speed, the shorter the wavelength, the
more frequently they pass
this means that the wavelength and frequency of electromagnetic waves
are inversely proportional
◦ since the speed of light is constant, if we know wavelength we can
find the frequency, and visa versa
c   
Calculate the wavelength of red light with a frequency of 4.62 x 1014 s-1
A laser dazzels the audience in a rock concert by emitting green light with a
wave length of 515 nm. Calculate the frequency of the light
10
Color



the color of light is determined by its
wavelength
◦ or frequency
white light is a mixture of all the colors
of visible light
◦ a spectrum
◦ RedOrangeYellowGreenBlueViolet
when an object absorbs some of the
wavelengths of white light while
reflecting others, it appears colored
◦ the observed color is predominantly
the colors reflected
11
The Electromagnetic Spectrum



visible light comprises only a small fraction of all the wavelengths of light
– called the electromagnetic spectrum
short wavelength (high frequency) light has high energy
◦ radiowave light has the lowest energy
◦ gamma ray light has the highest energy
high energy electromagnetic radiation can potentially damage biological
molecules
◦ ionizing radiation
12
The Photoelectric Effect
it was observed that many metals
emit electrons when a light shines
on their surface
◦ this is called the Photoelectric
Effect
 classic wave theory attributed this
effect to the light energy being
transferred to the electron
 according to this theory, if the
wavelength of light is made
shorter, or the light waves intensity
made brighter, more electrons
should be ejected

in experiments with the photoelectric
effect, it was observed that there was a
maximum wavelength for electrons to
be emitted
◦ called the threshold frequency
◦ regardless of the intensity
 it was also observed that high
frequency light with a dim source
caused electron emission without any
lag time

13
Particlelike Properties of
Electromagnetic Energy





Refers to the phenomenon in which
electrons are emitted from the surface of a
metal when light strikes it:
– No electrons are emitted by a given metal
below a specific threshold frequency νo.
– For light with frequency lower than the
threshold frequency, no electrons are
emitted regardless of the intensity of the
light.
– For light with frequency greater than the
threshold frequency, the number of
electrons emitted increases with the
intensity of the light.
– For light with frequency greater than the
threshold frequency, the kinetic energy of
the emitted electrons increases linearly with
the frequency of the light.
Einstein’s Explanation




Energy is in fact quantized and can be transferred only in discrete units
of size hν.
A system can transfer energy only in whole quanta
Einstein proposed that the light energy was delivered to the atoms in
packets, called quanta or photons
the energy of a photon of light was directly proportional to its frequency
◦ inversely proportional to it wavelength
◦ the proportionality constant is called Planck’s Constant, (h) and has
the value 6.626 x 10-34 J∙s
Ephoton  h 
15
hc

Ejected Electrons



1 photon at the threshold frequency has just enough energy for an electron
to escape the atom
◦ binding energy, f
for higher frequencies, the electron absorbs more energy than is necessary
to escape
this excess energy becomes kinetic energy of the ejected electron
Kinetic Energy = Ephoton – Ebinding
KE = h - f
16
Examples

he blue color in fireworks is often achieved by heating copper(I) chloride
(CuCl) to about 1200°C. The hot compound emits blue light having a wavelength of 450 nm. What is the increment of energy (the quantum) tha is
emitted at 450 nm by CuCl?

What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x 108
Hz?

Calculate the number of photons in a laser pulse with wavelength 337 nm and
total energy 3.83 mJ

What is the frequency of radiation required to supply 1.0 x 102 J of energy
from 8.5 x 1027 photons?
Spectra
when atoms or molecules absorb energy, that energy is often released as
light energy
◦ fireworks, neon lights, etc.
 when that light is passed through a prism, a pattern is seen that is unique to
that type of atom or molecule – the pattern is called an emission
spectrum
◦ non-continuous
◦ can be used to identify the material
 Rydberg analyzed the spectrum of hydrogen and found that it could be
described with an equation that involved an inverse square of integers

 1
1
1 
7
-1
 1.097 10 m  2  2 

 n1 n 2 

However, his equation gave little information into why atomic spectra were
discrete, why atoms are stable, or why his equation worked
18
Examples of Spectra
Oxygen spectrum
Neon spectrum
19
Emission vs. Absorption Spectra
Spectra of Mercury
20
Bohr’s Model



Neils Bohr proposed that the
electrons could only have very
specific amounts of energy
◦ fixed amounts = quantized
the electrons traveled in orbits that
were a fixed distance from the
nucleus
◦ stationary states
◦ therefore the energy of the
electron was proportional the
distance the orbital was from the
nucleus
electrons emitted radiation when
they “jumped” from an orbit with
higher energy down to an orbit
with lower energy
◦ the distance between the orbits
determined the energy of the
photon of light produced
21
Bohr Model of H Atoms
22
Wavelike Properties of Matter
Energy is really a form of matter, and all matter exhibits both particulate
and wave properties.
–Large “pieces” of matter, such as base balls, exhibit predominantly
particulate properties
–Very small “pieces” of matter, such as photon, while showing some
particulate properties through relativistic effects, exhibit dominantly wave
properties
–“Pieces” of intermediate mass, such as electrons, show both the
particulate and wave properties of matter
Louis de Broglie in 1924 suggested that, if light can behave in some
respects like matter, then perhaps matter can behave in some respects like
light.
In other words, perhaps matter is wavelike as well as particlelike.
= h
mv
examples

What velocity would an electron (mass = 9.11 x 10-31kg) need for its de
Broglie wavelength to be that of red light (750 nm)?

What is the velocity of an electron having a de Broglie wavelength that is
approximately the length of a chemical bond? Assume this length to be 1.2
x 10-10 m

Determine the wavelength of a neutron traveling at 1.00 x 102 m/s
(Massneutron = 1.675 x 10-24 g)
Quantum Mechanics and the Heisenberg
Uncertainty Principle

Heisenberg Uncertainty Principle – both the position (Δx) and the
momentum (Δmv) of an electron cannot be known beyond a certain level of
precision
1.
(Δx) (Δmv) > h
4π
2.
Cannot know both the position and the momentum of an
electron with a high degree of certainty
3. If the momentum is known with a high degree of certainty
i.
Δmv is small
ii.
Δ x (position of the electron) is large
4.
If the exact position of the electron is known
i.
Δmv is large
ii.
Δ x (position of the electron) is small
Determinacy vs. Indeterminacy

according to classical physics, particles move in a path determined by the
particle’s velocity, position, and forces acting on it
◦ determinacy = definite, predictable future

because we cannot know both the position and velocity of an electron,
we cannot predict the path it will follow
◦ indeterminacy = indefinite future, can only predict probability

the best we can do is to describe the probability an electron will be found
in a particular region using statistical functions
26