Download Objective 6: TSW explain how the quantum

Objective 6: TSW explain
how the quantum
mechanical model evolved
from Bohr’s model.
•Bohr’s model worked well only for
hydrogen or any atom with a single
electron
•Two things had to happen before the
quantum mechanical model was
developed
•Development of quantum mechanics
•Realization of the dual nature of
matter
•Max Planck developed quantum
mechanics in 1900
•He was studying how objects radiate
energy (heat)
•He discovered that the heat was being
given off in bursts of energy which are
called quanta
Classical vs. Quantum Mechanics
• Classical mechanics viewed energy transfer as
continuous
• When you drop an object from a height, the potential
energy it had at the height is continuously transferred to
kinetic energy as it falls and gains speed
• Quantum mechanics views energy transfer as
quantized
• The object at the height is in an energy state and when
you “drop” it, that energy is given off all at once and
moves to a lower energy state
Dual Nature of Matter
• Light has a dual nature, it has characteristics of
waves and of particle
• Wave characteristics include having a wavelength
(λ) and a frequency (f) and thus v = λf
• Waves can also form interference patterns in which
the amplitude of height of the wave is increased
(constructive interference) or decreased
(destructive interference) as the waves pass
through each other
• Light produces interference patterns when light
shines through diffraction gratings
• White light produces a rainbow effect
• Monochromatic light (light of a single frequency)
produces alternating areas of light and dark
• Technologies which take advantage of the wave
nature of light: laser-based surveying, holograms,
check-out-scanners, CDs and DVDs
• Particle characteristics of light include the ability to
reflect off of surfaces and that it has a speed
• Photoelectric effect: the ejection of electrons from a
metal surface when that surface is exposed to
electromagnetic radiation of sufficiently high
frequency
• In 1905 Einstein was able to explain the photoelectric
effect by using Planck’s quantum theory (for which he
won the Nobel prize in 1921)
• If light is being given off in bursts as Planck
suggested in quantum mechanics, it is a stream of
particles (photons) each with a specific amount of
energy, E = hf
• If the photon has sufficient energy to knock an
electron out of an atom, then it will be ejected, if it
isn’t of high enough energy nothing will happen
• Technologies which take advantage of the particle
nature of light: photography, photocopying
machines, photodiode technologies
• Just to clarify, light has a dual nature but it does
not and cannot exhibit both characteristics at the
same time: if you treat it like a wave, it will behave
like a wave and if you treat it like a particle, it will
behave like a particle
• In the 1920s, Louis de Broglie asked (and
answered) if light could behave both as a wave and
a particle, could particles such as electrons
demonstrate wave behaviors
• He connected demonstrated mathematically that it
was possible for a particle to have a wavelength
• de Broglie’s equation an equation which defines
the wavelength of a particle, λ = h/mv
• E = mc2
• E = hf
• mc2 = hf
• c is no longer the speed of light but the speed of a
particle and since the wave equation rearranged is f =
v/λ
• mv2 = hv/λ and rearranging and cancelling leads to de
Broglie’s equation: λ = h/mv
• The significance of the de Broglie equation is that it
demonstrates that particles have wave behaviors
• If you are dealing with an electron moving at
speeds near the speed of light you find it has a
sufficiently large wavelength so that its wavelength
is close to that of ordinary electromagnetic
radiation
• In the late 1920s, scientists observed electron
diffraction patterns thus confirming de Broglie’s
mathematics
Quantum Mechanical Model of the Atom
• In 1926, Erwin Schrödinger announced a new
model of the atom based on quantum mechanics
and probability
• He treated the electron not as a particle, but as a
wave
• Max Born added to the concept by saying that
since the electron was being treated as a wave, its
location could no longer being exactly defined
• The orbits proposed by Bohr were considered
electron waves and the electron wave
characteristics were directly related to the
probability of the location of an electron
• The location of an electron was represented as a
cloud (hence the reason the quantum mechanical
model is sometimes referred to as the “electron
cloud model”)
• These probability areas that represented a 95%
probability of finding the electron in that area were
now called atomic orbitals: area around the
nucleus where an electron is likely to be found
• In 1925, Werner Heisenberg suggested that it is
impossible to know both the exact location and
velocity of an electron at the same time
• That became known as the Heisenberg uncertainty
principle
• It confirms the concept of even though matter, like
light, has a dual nature, it cannot be both at the
same time
• If you treat the electron like a particle, you can
determine its location
• If you treat the electron like a wave, you can
determine its velocity
• Thus the quantum mechanical model of the atom
is a largely mathematical treatment of the behavior
of electrons in the area surrounding the nucleus
• The mathematics make it difficult to simplify