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Warm-Up: May 23/24, 2016
• Imagine you are given a 1 kg block of clay. Is it
possible to divide the block into continually
smaller and smaller pieces of clay without
limit? Why or why not?
Space Quiz
• Quiz on Kepler’s Laws, Planets, Stars, etc. next
class
• Mostly multiple choice
• Mostly conceptual/knowledge based
• Some computational questions on Kepler’s 3rd
Law (in various forms).
The Atom
Chapter 28
Origin of “Atom”
• Greek (and possibly Indian and Chinese)
philosophers around the 5th century BCE
questioned whether a substance can be
divided without limit into ever smaller pieces.
• Democritus in 5th century BCE believed there
was a smallest unit that cannot be further
subdivided. He called this the atom.
Brownian Motion
• In 1827, Robert Brown noticed that tiny pollen
grains suspended in still water moved about in
complex paths.
• The motion is caused by the random thermal
motions of water molecules colliding with the
pollen grain.
• The motion is now called Brownian Motion.
• By examining Brownian Motion, the size of
molecules can be calculated.
– Einstein explained how in 1905.
Brownian Motion
Parts of an Atom
• Nucleus
– Protons
• 𝑞𝑝 = 1.602 × 10−19 C
• 𝑚𝑝 = 1.673 × 10−27 kg
– Neutrons
• No charge
• 𝑚𝑛 = 1.675 × 10−27 kg
• Electrons
• 𝑞𝑒 = −1.602 × 10−19 C
• 𝑚𝑒 = 9.110 × 10−31 kg
J. J. Thomson
• Determined the ratio
𝑞𝑒
𝑚𝑒
• Determined the proton is about
1000 times more massive than
the electron.
• Believed that a massive,
positively charged substance
filled the atom, with electrons
distributed throughout the
positively charged substance
(like raisins in a muffin).
Rutherford’s Gold Foil Experiment
Rutherford’s Gold Foil Experiment
• Ernest Rutherford used a radioactive compound
that emitted alpha particles (𝛼-particles).
• The beam was directed at an extremely thin sheet
of gold foil.
• A flash of light was produced when an alpha particle
hit the surrounding screen.
• Rutherford was amazed that some alpha particles
bounced back.
– Rutherford compared his amazement to that of firing a
15-inch cannon shell at tissue paper and then having the
shell bounce back and hit him.
• Results published in 1909
The Nuclear Model
• Rutherford concluded that the atom’s positive
charges were concentrated in a tiny, massive
central core, now called the nucleus.
• Rutherford theorized that electrons orbit the
nucleus like planets orbit the Sun.
– This was later proven false
• Nuclear: of or relating to the nucleus
Atomic Emission Spectra (Iron)
Atomic Emission Spectra
• When emitted light is passed through a prism
or diffraction grating, the emission spectrum
is obtained.
• The spectrum of a hot body (i.e. filament in an
incandescent light bulb) is a continuous band.
• The spectrum of a gas is a series of distinct
lines.
More Emission Spectra
Absorption Spectra
• When light passes through a gas, certain
wavelengths are absorbed.
• These show up as dark lines in the spectrum.
• For a gas, the bright lines of the emission
spectrum and the dark lines of the absorption
spectrum often occur at the same
wavelengths.
Sodium Example
Problems with Planetary Model
• Electrons in orbit would constantly accelerate
towards the nucleus
– Think about centripetal acceleration from uniform
circular motion.
• Accelerating electrons radiate energy.
– This would cause the electron to spiral into the
nucleus in about 10−9 s.
– Radiated energy would be at all wavelengths, not
just the observed sprectrum lines.
Bohr Model of Atom
• Niels Bohr hypothesized that the laws of
electromagnetism do not apply inside an
atom.
• Bohr postulated that an electron in a stable
orbit, called a “stationary state,” does not
radiate energy.
– Only specific stationary states with specific energy
levels are allowed. (They must be quantized).
Energy of an Atom
• The energy levels of an atom are like stairs.
You may stand on any stair, but not at any
level in between.
• The smallest allowable energy level is the
ground state.
• Higher energy levels are excited states.
• Bohr suggested that energy is emitted when
the atom changes from one state to a lower
state.
Energy Levels
Energy Levels
Bohr Model
• Accurately predicts the wavelengths of light
emitted by hydrogen.
• Does not work for other elements.
• No explanation for why laws of
electromagnetism should not hold inside the
atom.
Energy of a Hydrogen Atom
13.6
𝐸𝑛 = − 2 eV
𝑛
• 𝑛 is the energy level, called the principal
quantum number.
• eV is the unit, not a variable.
• The unit eV is the electron-volt. It is the
amount of work done on an electron moving it
through one volt of electric potential
difference. 1 eV = 1.60 × 10−19 J
You-Try #1
a) Calculate the energies of the first six energy
levels of the hydrogen atom.
b) Calculate the energy difference between 𝐸3
and 𝐸2 . Express your answer both in joules
and electron-volts.
c) Calculate the energy difference between 𝐸6
and 𝐸3 . Express your answer both in joules
and electron-volts.
Wavelength of Emitted Light
𝜆=
ℎ𝑐
𝐸𝑝ℎ𝑜𝑡𝑜𝑛
• 𝜆 is the wavelength
• ℎ is Planck’s constant, 6.626 × 10
−34 𝑚2 𝑘𝑔
𝑠
• 𝑐 is the speed of light in a vacuum
• 𝐸𝑝ℎ𝑜𝑡𝑜𝑛 is the energy of the photon
• Equal to the energy released by the atom
• 𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = −Δ𝐸𝑎𝑡𝑜𝑚
• Photon is the particle of light.
You-Try #2
• Which changes in hydrogen energy levels
produce visible light? List all correct answers
that involve 1st through 6th energy levels.
Assignment
• Read Section 28.1 (pages 747-759)
• Page 770 #23-26, 29-30, 43-48, 55
• Optional advanced reading: OpenStax
Chapter 30
May 25/26, 2016: Quiz Time!
• Clear everything off of your desk except
writing utensils, erasers, and your calculator.
• Make sure all electronic devices are powered
off and in your backpack.
May 25/26, 2016: Quiz Time!
• 20 minute time limit
• If you appear to be talking, looking at anyone
else’s quiz, allowing another student to look at
your quiz, or using any unauthorized aide, you
will receive a zero.
• If any electronic device is seen or heard, it
goes to the office and you will receive a zero.
• When finished, turn in your quiz to Mr. Szwast
and prepare to take notes on Section 28.2
Homework Questions?
The Quantum Model of the Atom
Section 28.2
Louis de Broglie
• In 1923, French physicist Louis de Broglie
proposed that material particles have wave
properties.
– Was proven for electrons in 1927.
• The de Broglie wavelength of a moving particle is
given by
ℎ
𝜆=
𝑚𝑣
−34 𝑚2 𝑘𝑔
Where ℎ is Planck’s constant, 6.626 × 10
𝑠
Heisenberg Uncertainty Principle
• It is impossible to measure precisely both the
position and momentum of a particle at the
same time.
– The more accurately you measure one, the less
accurately you can measure the other.
• Named for German physicist Werner
Heisenberg.
• This contradicts the well-defined orbits of
Bohr’s model.
Bohr Model Revisited
• Because of the wave-like properties of
electrons, electrons can only exist where they
interfere constructively.
• For a circular orbit, the circumference of the
orbit must be a whole-number multiple of the
de Broglie wavelength.
Bohr Model Revisited
Erwin Schröedinger
• In 1926, Austrian physicist Erwin Schröedinger
used de Broglie’s wave model to create a
quantum theory of the atom based on waves.
• In accordance with the Heisenberg
uncertainty principle, the modern quantum
model of the atom predicts only the
probability that an electron is in a specific
region.
Schröedinger’s Cat
What does quantum mean?
• A quantum is the lowest possible value of
something.
• If a physical property is quantized, then it may
only take on certain discrete values, that are
integer multiples of the lowest quantum
value.
• All charges being integer multiples of the
charge of an electron is one example.
Quantum Model
• The most probable distance
between the electron and
nucleus of hydrogen is the same
as the radius predicted by the
Bohr model.
• The region where there is a high
probability of finding an
electron is called the electron
cloud.
Quantum Mechanics
• Quantum mechanics is the study of the
properties of matter using its wave properties.
• Uses the quantum model of the atom.
• Has led to many advances in chemistry and
physics, including lasers.
Stimulated Emission
• An atom in an excited state can release a
photon.
• If that photon strikes another atom in the
same excited state, it releases a second
photon with the same frequency and in-step
– This causes constructive interference.
• If enough atoms start in the same excited
state, this causes a cascade of photons, all
with the same frequency and in-step.
Lasers
• Invented in 1959
• Light Amplification by Stimulated Emission of
Radiation
• Very inefficient
– Gas lasers convert less than 1% of electrical
energy into light energy
– Crystal lasers convert ~20% of electrical energy
into light energy
Think-Pair-Share
• What are some applications of lasers? Write
down as many as you can think of.
Applications of Lasers
•
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CD/DVD/Blu-ray players
Bar code readers
Entertainment laser shows
Laser printers
Fiber optics
Surveying
Surgery
Welding
Holograms
Laser tag
Assignments
• Read Section 28.1 (pages 747-759)
• Page 770 #23-26, 29-30, 43-48, 55
• Read Section 28.2 (pages 760-769)
• Page 770 #31-33, 41-42, 57-60
• Optional advanced reading: OpenStax
Chapter 30