Download Unit 3: Atomic Theory & Quantum Mechanics Section A.3

Unit 3: Atomic Theory & Quantum
Mechanics
Sections A.4 – A.5
In which you will learn about:
•Blackbody Radiation
•The photoelectric effect
•Atomic emission spectra
•The Bohr Model of the Atom
A.4 The Particle Nature of Light
 Considering light as a wave explains much of its everyday
behavior
 It does NOT explain how light interacts with matter. For
example…
 Doesn’t explain why heated objects only emit certain frequencies of light
at a given temperature (blackbody radiation)
 Doesn’t explain why some metals emit electrons when light of a specific
frequency shines on them (photoelectric effect)
Blackbody Radiation
 When objects are heated, they emit glowing light
 Temperature = average kinetic energy of particles
 As the iron in the picture gets hotter, it possesses a greater amount
of energy and emits different colors of light which correspond to
different frequencies and wavelengths (red to orange to bluish)
The Quantum Model
 The wave model could not explain the emission of these




different wavelengths
In 1900, Max Planck (1858-1947) began to research this
phenomenon
His results showed that matter can gain or lose energy only in
small, specific amounts, called quanta.
Quantum = the minimum amount of energy that can be
gained or lost by an atom
Remember, light = electromagnetic radiation = energy.
Why is the quantum idea so weird?
 Planck and other physicists of the time thought the concept of
quantized energy was revolutionary, and some found it disturbing.
 Think of it this way…
 You’re heating a cup of water in a microwave
 You should be able to add any amount of thermal energy to the water
by regulating the power and the time the microwave is on (ok, normal
so far…)
 Instead, the water’s temperature increases in infinitesimally small
steps as its molecules absorb quanta of energy
 Because the steps are so small, the temp. rise seems continuous,
rather than stepwise
Energy of a Quantum
 Quantum = discrete amount of energy = packet of energy =
packet of light = photon
Ephoton = hν
 E = energy
 h = Planck’s constant = 6.626 x 10-34 J∙s
 ν = frequency
 NOTE: J stands for Joule, which is the SI unit for energy
 NOTE 2: As energy increases, frequency increases. They
are directly proportional.
Quantum Analogy
 Think of a child building a wall of wooden blocks
 The child can add or take away height from the wall only in
increments of whole numbers of blocks
 Similarly, matter can only have certain amounts of energy—
quantities of energy between these values do not exist
 OR, think of a ladder. To climb it, you must place your feet
on each rung, but you can’t step up using the space between.
Example Problem - GUESS
 Every object gets its color by reflecting a certain portion of incident






light. The color is determined by the wavelength of the reflected
photons, thus by their energy. What is the energy of a photon from the
violet portion of the Sun’s light if it has a frequency of 7.230 x 1014 1/s?
G: ν = 7.230 x 1014 1/s & h = 6.626 x 10-34 J∙s
U: E = ?
E: E = hν
S: E =(6.626 x 10-34 J∙s)(7.230 x 1014 1/s)
S: 4.791 x 10-19 J
This answer makes sense, because although the energy is very small, it is
the energy of ONE photon of violet light.
The Photoelectric Effect
 Scientists also knew that the wave model of light could not explain a
phenomenon called the photoelectric effect.
 Photoelectric effect = electrons (called photoelectrons) are emitted
from a metal’s surface when light of a certain frequency shines on the
surface
 This effect does NOT depend on the intensity (brightness of the light)
 This effect does NOT depend on how long the light shines
 The light MUST be at the threshold frequency or higher for the effect to
work
 Every metal has it’s own threshold frequency – for example, potassium will eject
electrons when green light shines on it, but beryllium will not.
The Photoelectric Effect
Light’s Dual Nature
 To explain the photoelectric effect, Albert Einstein proposed in
1905 that light has a dual nature
 A beam of light has wavelike and particle-like properties.
 It can be thought of as a beam of bundles of energy called photons.
 Photon = mass-less particle that carries a quantum of energy
 Einstein calculated that the energy of a photon must have a certain
threshold value to cause the ejection of the photoelectron from
the surface of the metal.
 Even small numbers of photons with energy above the threshold value
will cause the photoelectric effect
 Einstein won the Nobel Prize in Physics in 1921 for this work (not for
E=mc2 or special relativity!)
Wave-Particle Duality
 Most people get confused with the idea of light being both a
wave and a particle. I think of it like this (must watch this one
on the comp!):
Optical illusions are also two things
simultaneously!
Neon Signs
 Have you ever wondered how light is produced in the
glowing tubes of neon signs?
 This process is another phenomenon that cannot be explained
by the wave model of light
 The light of the neon sign is produced by passing electricity
through a tube filled with neon gas.
 Neon atoms in the tube absorb energy and become excited
(unstable)
 These excited atoms return to their stable (ground) state by
emitting light to release that energy.
 Neon signs only produce red! Other colors that are in “neon”
signs are actually different gases.
Atomic Emission Spectra
 If the light emitted by the neon is passed through a glass
prism, neon’s atomic emission spectrum is produced.
 Atomic emission spectrum = the set of frequencies of the
electromagnetic waves emitted by atoms of the element (see
below for neon’s—3rd from top—spectrum)
Atomic Spectra Up Close
What to look for in Atomic Emission
Spectra
 Neon’s atomic emission spectrum consists of several
individual lines of color corresponding to the frequencies of
radiation emitted by the atoms of neon
 Note that it is NOT a continuous range of colors, such as the
spectrum for sunlight (white light).
 Each element’s atomic emission spectrum is unique and can
be used to identify an element or determine whether that
element is part of an unknown compound (we’ll be
conducting a lab on this during our next long block!)
A.5 Bohr’s Model of the Atom
 The dual wave-particle model of light accounted for several
previously unexplainable phenomena, but scientists still did not
understand the relationship among atomic structure, electrons,
and atomic emission spectra.
 Recall the hydrogen’s atomic emission spectrum is discontinuous; that
is, it is made up of only certain frequencies of light – WHY??
 Niels Bohr, a Danish physicist working in Rutherford’s laboratory
in 1913, proposed a quantum model for the hydrogen atom that
seems to answer this question.
 His model also correctly predicted the frequencies of the lines in
hydrogen’s atomic emission spectrum
Energy States of Hydrogen
 Bohr proposed that the hydrogen atom has only certain
allowable energy states.
 Ground state = the lowest allowable energy state
 Excited state = when at atom gains energy, its electrons are in
this state
Bohr’s Planetary Model WITH Orbits
 Bohr related the hydrogen atom’s energy states to the
electron within the atom.
 He suggested that the electron in a hydrogen atom moves
around the nucleus in only certain allowed circular orbits.
 The smaller the electron’s orbit, the lower the atom’s energy
state, or energy level. The converse is also true.
 Hydrogen can have many different excited states, although it
only contains one electron (but it can only have one ground
state).
Quantum Numbers
 In order to complete his calculations, Bohr assigned a
number, n, called a quantum number, to each orbit.
Bohr’s
Atomic
Orbit
Quantum
Number
Orbit Radius
(nm)
Corresponding
Atomic Energy
Level
Relative
Energy
First
n=1
0.0529
1
E1
Second
n=2
0.212
2
E2 = 4E1
Third
n=3
0.476
3
E3 = 9E1
Fourth
n=4
0.846
4
E4 = 16E1
Fifth
n=5
1.32
5
E5 = 25E1
Sixth
n=6
1.90
6
E6 = 36E1
Seventh
n=7
2.59
7
E7 = 49E1
The Hydrogen Line Spectrum
 Bohr suggested that the hydrogen atom is in the ground state, also called
the first energy level, when its single electron is in the n = 1 orbit.
 In the ground state, the atom does not radiate energy.
 When energy is added from an outside source, the electron moves to a
higher-energy orbit, such as n = 2.
 Such an electron transition raises the atom to the excited state.
 When the atom is in the excited state, it can drop from the higher-
energy orbit to a lower-energy orbit.
 As a result of this transition, the atom emits a photon corresponding to the
energy difference between the two levels.
 ΔE = Ehigher-orbit – Elower-orbit = Ephoton = hν
Hydrogen Further Explained
 Because only certain atomic energies are possible, only
certain frequencies of electromagnetic radiation can be
emitted (hence, the discontinuous lines on the spectrum).
Note the 4 Colored Lines…
Balmer, Lyman, Paschen Series
 In the previous slide, it was shown that the four colored lines in
the hydrogen spectrum are a result of the electron moving from
energy levels




6  2 = purple line
5  2 = blue line
4 2 = green line
3  2 = red line
 These are the only transitions in the VISIBLE spectrum
 Other transitions can occur. If the electron goes from
 Excited state  1 = Lyman Series (only seen in UV)
 Excited state  2 = Balmer Series (only seen in visible)
 Excited state  3 = Paschen Series (only seen in IR)
The Limits of Bohr’s Model
 Bohr’s model explained hydrogen’s observed spectral lines
 But it failed to explain the spectrum of any other element! (too many
electrons to consider)
 Bohr’s model also does not account for the chemical behavior of atoms
 In fact, although Bohr’s idea of quantized energy levels laid the
groundwork for atomic models to come…
 Later experiments showed that the Bohr model was fundamentally incorrect!
(And now we have to re-teach you everything you ever learned about atoms,
isn’t this fun?)
 The movements of electrons in atoms are not completely understood even
now; however, evidence indicates that electrons do NOT move around the
nucleus in circular orbits.
A.4 Homework Questions
 1) Calculate the energy possessed by a single photon of each of the
following types of electromagnetic radiation.
 a) 6.32 x 1020 1/s
 b) 9.50 x 1013 Hz
 c) 1.05 x 1016 1/s
 2) The blue color in some fireworks occurs when copper (I)
chloride is heated to approximately 1500 K and emits blue light of
wavelength 4.50 x 102 nm. How much energy does one photon of
this light carry? (HINT: Use both light equations we’ve learned so
far!)
 CHALLENGE: The microwaves used to heat food have a
wavelength of 0.125 m. What is the energy of one photon of the
microwave oven?
A.4 Homework Questions Cont’d
 3) Compare the dual nature of light.
 4) Describe the three phenomena that can only be explained
by the particle model of light.
A.5 Homework Question
 5) Explain the reason, according to Bohr’s atomic model,
why atomic emission spectra contain only certain frequencies
of light.