Transcript Section 5.3 Physics and Quantum Mechanical Model

Section 5.3
Physics and Quantum Mechanical
Model
• The study of light led the development
of the quantum mechanical model by
Schrödinger’s.
• Isaac Newton believed that light
consisted of particles.
• Scientists in the beginning of the 1900’s
believed that light consisted of waves.
Parts of a Wave
• Amplitude: height from zero to the crest.
• Wavelength (λ): the distance between the crests.
• Frequency (υ): the number of wave cycles to pass a
given point per unit of time.
• Speed of light (c) equals the wavelength times the
frequency
c=λυ
• The wavelength and frequency of light
are inversely proportional to each other.
c=λυ
• According to the wave model, light
consists of electromagnetic waves.
• Electromagnetic radiation includes radio
waves, microwaves, infrared waves,
visible light ultraviolet waves, X-rays,
and gamma rays.
• All electromagnetic waves travel in a
vacuum at a speed of 2.998 X 108m/s.
Color Spectrum
• Sunlight (white light) is a continuous range of
wavelengths and frequencies.
• A prism, or rain droplets in the case of a
rainbow, can separate each frequency of light
into a spectrum of colors.
• Each color bends into the other in the order of
red, orange, yellow, green, blue, and violet.
– ROY G BIV
• Which color in the visible spectrum has the
longest wavelength?
Practice Problem
Calculating the Wavelength of Light
Question
• What is the frequency of
radiation which has a
wavelength of 7.00 X 10-5
cm?
• In what region of the
electromagnetic spectrum
is this radiation?
Answer
• 4.29 X 1014 s-1
• Infrared
Spectrum
Atomic Spectra
• When atoms absorb energy, electrons
move into higher energy levels, and these
electrons lose energy by emitting light
when they return to lower energy levels.
• Unlike white light, the light emitted by
atoms consists of a mixture of only specific
frequencies, each of a particular color.
• Therefore, when light emitted by an
element passes through a prism, it
separates into discrete lines to give the
atomic emission spectrum of that
element.
Atomic Emission Spectrum
• Each discrete line in an emission spectrum
corresponds to one exact frequency of
light emitted by the atom.
• Each emission spectrum is unique to that
element. No two elements have the same
spectrum.
Niels Bohr
• The Bohr Model, was
on of the first models
to explain the
emission spectrum of
hydrogen, and
predicted specific
values of these
frequencies.
• In the Bohr models the
lone electron of hydrogen
can have only certain
specific energies.
• The lowest energy is its
ground state
• In the ground state the
principle quantum
number (n) is 1.
• Excitation of the electron
by absorbing energy
raises it from quantum
from the ground state to
an excited state with n =
2, 3, 4, and so forth.
Ground State
Emission of Light
• When the electron
looses energy and
drops back to a
lower energy level,
energy (in the form
of light) is
released.
• This happens in a
single abrupt step
called an electronic
transition.
Energy Equation
• The light emitted by an
electron moving from a
higher to a lower energy
level has a frequency
directly proportional to
the energy change of the
electron.
• Therefore, each each
transition produces a line
of specific frequency ()
in the spectrum
Energy is related by:
E = (h)()
where; h = 6.626 X 10-34 J
s
plan
 = frequency
3 Groups of Lines Observed in the
Emission Spectrum of Hydrogen
Refer to Page 143 Figure 5.14
1. Lyman Series
•
•
Ultraviolet
Energy value of electrons from higher energy
levels to n =1
2. Balmer Series
•
•
Visible
transitions from higher energy levels to n = 2
3. Paschen Series
•
•
Infrared
transitions from higher energy levels to n = 3
Questions
1.
2.
3.
4.
5.
6.
What is the name of the series of visible lines in
the hydrogen spectrum?
Suppose an electron, in its ground state at n = 1,
absorbs enough energy to jump to n = 2. What
type of radiation will it emit when it returns to the
ground state?
If you observe a hydrogen gas discharge tube
through a diffraction grating, could you see the line
corresponding to this emission?
Which series of lines could human detect with our
eyes?
Compare the energy of the Paschen and the
Balmer series.
What do you notice about the spacing of the
energy levels from n = 1 to n = 7?
Quantum Mechanics
• Light – is it a wave or a particle?
• Dual Wave-Particle Behavior of light
• The particle aspect (as explained by
Einstein) of light, could be describe as a
quanta of energy.
• Light quanta are called photons
Photoelectric Effect
• Metals eject electrons called
photoelectrons when light
shines on them.
• Red light ( = 4.3 X 1014 s-1 to
4.6 X 1014 s-1), will not cause
the ejection of
photoelectrons from
potassium metal.
• Yellow light ( = 5.1 X 1014 s-1
to 4.3 X 1014 s-1) will.
• Intensity does not matter.
De Broglie
• Reasoned that if light behaves as waves and
particles, than particles of matter can also behave
as waves.
= h
(m)()
where;
h = plank’s constant (6.626 X 10-34 J s)
m = mass
 = frequency
• Classical mechanics adequately describes the
motions of bodies much larger than atoms, while
quantum mechanics describes the motion of
subatomic particles and atoms as waves.
• Using the above equation, the wavelength of a
moving electron (mass of an electron is 9.11 X 10-28g)
and (moving at the speed of light) has a wavelength of
about 2 X 10-10cm. (this is the size of a typical atom)
Major Differences between
Classical Mechanics and
Quantum Mechanics
1. Classical mechanics adequately
describes the motions of bodies much
larger than the atoms they comprise. It
appears that such a body gains or loses
energy in any amount.
2. Quantum mechanics describes the
motions of subatomic particles and atoms
as waves. These particles gain or lose
energy in packages called quanta.
Heisenberg Uncertainty
Principle
• It is impossible to know exactly both the
velocity and the position of a particle at the
same time.
• Schrödinger used the wavelike motion of
matter and the uncertainty principle in his
electron cloud model of an atom which
lead to the concept of electron orbitals and
configurations.