Electrons!
Chapter 5
I.Light & Quantized Energy
A.Background
1. Rutherford’s nuclear model: nucleus
surrounded by fast-moving electrons; no info
on how electrons move, how they’re
arranged, or differences in chemical behavior
a. Example: Cl, Ar, K are #s 17, 18, 19 -consecutive atomic numbers, but very
different properties -- why?
2. Early 1900s: scientists noticed that some
elements produced light when placed in a
flame
a. Analyzing the specific light emitted
showed that chemical behavior was
related to electron arrangement
B. Light: Wave Nature
1. Wavelength (λ): distance between two neighboring crests or troughs
a. unit: usually nanometers (1 x 10-9 m = 1 nm)
2. Frequency (ν): number of waves (measured in # of crests) which pass a given
point each second
a. unit: hertz (1 Hz = 1 wave/second), kilohertz, megahertz
b. in mathematical calculations, use s-1 (1 s-1 = 1 Hz)
3. Amplitude: height of wave from origin to crest or origin to trough
4. Speed of light (c) = 3.00 x 108 m/s
c = λν
^see p. 119
i. Example: A certain red light has a wavelength of 650 nm. What is its
frequency?
(BRINGIN’ BACK G.U.E.S.S)
G: wavelength = 650 nm, c = 3.00 x 108 m/s, 1 Hz = 1 s-1
U: frequency (in Hz)
E: c = λν
can change to ν = c/λ
S: 3.00 x 108 m
1 nm
1
1 Hz
1s
1 x 10-9 m
650 nm
1 s-1
S: 4.62 x 1014 Hz
5. Electromagnetic (EM) radiation: form of energy released by EM processes that acts
like a wave as it travels through space; consists of synchronized electric &
magnetic fields
a. Electromagnetic (EM) spectrum: spectrum of all EM radiation resulting from
fluctuations or vibrations of charged particles (p. 120)
i. Includes radio waves, microwaves, radar waves, infrared light, visible light
(aka continuous spectrum),
ultraviolet, X-rays, and gamma rays
ii. Each part of the continuous
spectrum corresponds
to a specific wavelength
& frequency, which are
refracted at different
angles -- produces
colors (ROY G BIV)
Practice Problems: p. 121, #1-4
C. Light: Particle Nature
1. Wave model of light does not describe all of its interactions with matter, like
iron emitting different wavelengths of light (colors) at different temperatures -so how can these interactions be explained?
2. Max Planck (German physicist, 1890s) wanted to figure this out!
a. Studied light emitted from heated objects
b. Found that frequencies & energy changed in tiny, specific amounts, and
matter can only gain or lose energy in these small amounts (quanta), NOT
in any random amount
c. Quantum: minimum amount of energy that can be gained or lost by an
atom; plural quanta; also called photons
d. All energy, including light, comes in quanta -- this is quantum theory
e. Each color of light has a specific sized quanta; red is small, violet is large
3. Planck proposed a formula that expresses the energy of a single quantum
(photon) of radiation of any given frequency
E = energy (in joules)
E = hν
h = Planck’s constant, 6.626 x 10-34 J⋅s
ν = frequency in s-1
a. Example: how much energy is contained in one quantum of a gamma ray?
Frequency of gamma ray is 1 x 1024 Hz
G: h = 6.626 x 10-34 J⋅s, ν = 1 x 1024 Hz, 1 Hz = 1 s-1
U: energy (in joules)
E: E = hν
S: 6.626 x 10-34 J⋅s 1 x 1024 Hz
1 s-1
1
1
1 Hz
S: 6.626 x 10-10 J
b. Example 2: how much energy is contained in one quantum of a radio
wave? Frequency of radio wave is 1 x 104 Hz
4. Albert Einstein (German physicist,
1905) studied the photoelectric
effect: light of a certain frequency
(color) shining upon a material &
causing electrons to be discharged
from the material
a. Theoretically, a very lowfrequency light directed at a
material for a long period of
time will eventually accumulate
& provide enough energy for
the material to eject electrons…
BUT, that didn’t happen -- why?
b. Einstein found that when the intensity of light of a particular wavelength
was reduced, fewer electrons were ejected, & vice versa
i. Based on wave theory, less intense light should cause electrons to be
ejected with lower kinetic energy, & vice versa
ii. However, electrons emitted at lower intensities still had the same
kinetic energy as when the intensity was greater
iii.Conclusions:
● Light has both wave & particle properties
● Light consists of photons: particles of EM radiation carrying a
quantum of energy (plain English: light is a stream of tiny
bundles of energy)
● Photons have their own specific energy for a given wavelength;
at minimum, one photon possesses the energy necessary to eject
an electron from a material
Practice Problems: p. 124, #5-6
Homework: p. 126, #7-12
Homework Answers
p. 873
3) 3.61 x 10-19 J
4) 8.48 x 10-16 J
5a) 4.19 x 10-13 J
5b) 6.29 x 10-20 J
5c) 6.96 x 10-18 J
6a) gamma ray or X ray
6b) infrared
6c) ultraviolet
p. 124
p. 126
7.
8.
speed, wavelength, frequency, amplitude; EM waves travel at c
Wave model treats light as an EM wave; particle model treats it as comprised of photons.
Wave model couldn’t explain photoelectric effect, color of hot objects, & emission spectra.
9. A quantum is the minimum amount of energy that can be lost or gained by an atom; matter
loses or gains energy in multiples of the quantum
10. Continuous spectrum contains all colors, emission spectra contains only specific colors
11. Einstein proposed that EM radiation has a wave-particle nature, that the energy of a photon
depends on the frequency of the radiation, and that a photon’s energy is given by E photon = hv
12. a: 3 (radio waves)
b: 1 (gamma rays)
c: 1 (gamma rays)
D. Light Spectra
1. Light is not always absorbed or emitted by a material continuously, as the wave
model would suggest -- instead, it is often emitted in bursts by excited
electrons
2. Atomic emission spectrum: frequencies of light emitted by a given material
a. When substances are passed through a flame, they glow a particular color
(example: copper - green, sodium - yellow)
b. When this light is passed through a prism & divided, a series of colored
lines appears called spectral lines
c. Each element has a unique set of lines it produces, so atomic emission
spectra (the sets of lines) can be used to identify elements
d. Example: hydrogen’s emissions spectrum, p. 126
II. Quantum Theory & the Atom
A.Bohr’s Model
1. Proposed a quantum atomic model that explained why atomic emission spectra
are only made up of certain frequencies of light, not all continuously
2. Key points:
a.
b.
c.
d.
e.
f.
There are certain definite orbits in which electrons can travel
An electron in a given orbit has a certain definite amount of energy
The greater the distance from the nucleus, the greater the energy of the electron
Possible electron orbits are called energy levels
An electron can gain energy from various sources, causing it to “jump” to a higher level
When an electron drops to a lower energy level, it loses energy in the form of a photon
of radiation
g. Energy of the photon corresponds to the difference in energy levels
h. An electron cannot drop into an energy level which already holds its maximum
number of electrons
3. Also mapped out energy levels
a. Lowest energy level is called the ground state
b. When an atom gains energy, it enters an excited state –
Bohr described 7 possible excited states/energy levels of
hydrogen & assumed it was the same for other atoms
c. Atom gains energy  electrons “jump” to higher energy
levels
d. Atom loses energy in the form of a photon of EM radiation
 electrons “fall” back to a lower energy level
e. Amount of energy photon carries is determined by the
difference in energy levels when an electron “falls” from
an upper level to a lower level
ΔE = E higher-energy orbit – E lower energy orbit = E photon = hf
B. Quantum-Mechanical Model
1. Bohr’s model explained hydrogen well, but not really other elements; primarily
his ideas of quantized energy & energy levels were correct & expanded upon by
several scientists
2. Louis de Broglie suggested that all moving particles have wave properties
a. de Broglie equation: λ = h/mv wavelength of any particle is equal to Planck’s
constant divided by mass times velocity
b. He was correct!
3. Heisenberg’s uncertainty principle: there is always some uncertainty as to the
location & velocity of an electron – it is impossible to know both simultaneously
4. Schrödinger treated electron as a wave & came up with an equation to describe
its wave-like behavior – confirmed electron has both wave & particle properties
5. Wave model predicts that electrons will be found in an atomic orbital: a 3D
region around the nucleus
C. Hydrogen’s Atomic Orbitals
1. Principal quantum number (n): indicates sizes & energies of atomic orbitals
a. Corresponds to the energy levels suggested by Bohr (1,2,3,4,5,6,7) – called principal
energy levels
b. Electrons may be found in each energy level of an atom (7 shown on the periodic table)
c. Largest possible number of electrons possible in any one level is 2n2
2. Energy sublevels: contained within principal energy levels
a.
b.
c.
d.
Number of sublevels contained within each principal energy level = n
All electrons in each energy level do not have the same energy as earlier assumed
Determines the shape of the electron cloud
Four types of sublevels are possible, each with a defined shape & number of electrons:
s “sharp”: lowest sublevel
2e- (1 pair)
p “principal”: second sublevel
6e- (3 pair)
d “diffuse”: third sublevel
10e- (5 pair)
f “fundamental”: fourth sublevel
14e- (7 pair)
Copy in notes:
• Table 5-1
• Figure 5-10 a & b