Download Energy, Heat, and Work* Oh My*

Alcatraz is Closed (1963)
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Reading for Wednesday
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HOMEWORK – DUE Wednesday 3/22/17
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EXP 10
Lab Wednesday/Thursday
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WS 12 (Worksheet): (from course website)
CH 7 EC: 5, 7, 8, 9, 11, 12, 14, 15, 20, 21, 24, 29, 30, 31, 34, 39, 50, 51, 52, 55-59 all, 64, 69, 71, 72, 90
Lab Today/Tomorrow
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WS 11 (Worksheet): (from course website)
HOMEWORK – DUE Monday 3/27/17
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Chapter 8 sections 1-2
Open office hours
Exam 3 NEXT Monday
Spectra

When atoms or molecules absorb energy, that energy is often
released as light energy


fireworks, neon lights, etc.
When that emitted light is passed through a prism, a pattern of
particular wavelengths of light is seen that is unique to that type of
atom or molecule – the pattern is called an emission spectrum
non-continuous
 can be used to identify the material

Examples of Spectra
The Bohr Model of the Atom

The energy of the atom is quantized, and the amount of energy in the atom is
related to the electron’s position
 quantized

means that the atom could only have very specific amounts of energy
The electron’s positions within the atom (energy levels) are called stationary
states
 Each
state is associated with a fixed circular orbit of the electron around the nucleus.
 The higher the energy level, the farther the orbit is from the nucleus.

 The
The first orbit, the lowest energy state, is called the ground state.
atom changes to another stationary state only by absorbing or emitting a photon.
 Photon energy (hn) equals the difference between two energy states.
The Bohr Model of the Atom
-
5 4
3
2
1
nucleus
-
-
Emission Spectra
Bohr Model of H Atoms
Emission Spectra
Hydrogen Energy Transitions
Which is a higher energy transition?
65 or 32
6
5
53 or 31
23 or 34
4 3
2
1
nucleus
Rydberg’s Spectrum Analysis

Rydberg developed an equation involved an inverse square of integers that
could describe the spectrum of hydrogen.
 1
1 
 R  2  2 
n


n
 1
2 
1
1.096776  107
R 
m
What is the wavelength (nm) of light based on an electron transition from n = 4 to n = 2?
1.0968  107


m
1
 1
1 
 2  2 
2 
4

1


2056875
m
HUH?!?!?

  486 nm
Wave Behavior of Electrons


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de Broglie proposed that particles could have wave-like character
Predicted that the wavelength of a particle was inversely proportional to its
momentum
Because an electron is so small, its wave character is significant
hc
E=
hc
h
h
2

= mc
=
λ=

mc
mv
2
E = mc
h = planks constant
Js
kg  m 2
s2
s
m = mass of particle
kg
v = velocity
m
s
What is the wavelength of an electron traveling at 2.65 x 106 m/s.
(mass e- = 9.109x10-31 kg)
h
λ=
mv
λ=
2
34 kg m
6.626  10
s
31
9.109  10
kg  2.65  106
m
s
 2.745  1010 m
Determine your wavelength if you are walking at a pace of 2.68 m/s.
(1 kg = 2.20 lb)
λ=
2
34 kg m
6.626  10
s
91.8 kg  2.68 ms
 2.96  1036 m
The Quantum Mechanical Model of the Atom
The matter-wave of the electron occupies the space near the nucleus and is
continuously influenced by it.
The Schrödinger wave equation allows us to solve for the energy states
associated with a particular atomic orbital.
 h2

 8 me
 2
2
2
 2  2  2
y
z
 x


  V  x, y, z   Ψ  x, y, z   EΨ


HΨ  EΨ
The square of the wave function (Y2) gives the probability density, a measure of the
probability of finding an electron of a particular energy in a particular region of the atom.
Probability & Radial Distribution Functions

y2 is the probability density



The Radial Distribution function represents the total probability at a certain
distance from the nucleus


the probability of finding an electron at a particular point in space
decreases as you move away from the nucleus
maximum at most probable radius
Nodes in the functions are where the probability drops to 0
Probability Density Function
The probability density function represents the total probability of
finding an electron at a particular point in space
Radial Distribution Function
The radial distribution function represents the total probability
of finding an electron within a thin spherical shell at a distance r
from the nucleus
The probability at a point decreases with increasing distance
from the nucleus, but the volume of the spherical shell increases
The net result is a plot that indicates the most probable distance
of the electron in a 1s orbital of H is 52.9 pm
Solutions to the Wave Function, Y
Calculations show that the size, shape, and orientation in space of an
orbital are determined to be three integer terms in the wave function
 These integers are called quantum numbers

principal quantum number, n
 angular momentum quantum number, l
 magnetic quantum number, ml

Principal Quantum Number, n

Characterizes the energy of the electron in a particular orbital and the size of
that orbital




n can be any integer  1
The larger the value of n, the more energy the orbital has
The larger the value of n, the larger the orbital



corresponds to Bohr’s energy level
Greater relative distance from the nucleus
As n gets larger, the amount of energy between orbitals gets smaller
Energies are defined as being negative

an electron would have E = 0 when it just escapes the atom
Principal Quantum Number, n

The energies of individual energy levels in the hydrogen atom (and therefore
the energy changes between levels) can be calculated.
En  hcR
1
n2
 1
1
E  hcR  2  2
 n final ninitial





What is the energy of a photon of light based on an electron transition from n = 4 to n = 2?
34
19 7 
 8m
2.180
6.62610
1018
JJ s  2.998
1
1 10
4.087
1.0968
 1010
J
1
1 
EE44
 
  2  2   
 2  2 
22 


2
photon
photon
photon
m
4s 
4 
2

Principal Energy Levels in Hydrogen
Angular Momentum Quantum Number, l



The angular momentum quantum number determines the shape of the orbital
l can have integer values from 0 to (n – 1)
Each l is called by a particular letter that designates the shape of the orbital




s (spherical) orbitals are spherical
p (principal) orbitals are like two balloons tied at the knots
d (diffuse) orbitals are mainly like four balloons tied at the knot
f (fundamental) orbitals are mainly like eight balloons tied at the knot
principal (n) quantum number
1
2
3
4
5
possible angular momentum (l) quantum number(s)
0 (s)
0, 1 (s, p)
0, 1, 2 (s, p, d)
0, 1, 2, 3 (s, p, d, f)
0, 1, 2, 3, 4 (s, p, d, f, g)
Magnetic Quantum Number, ml

The magnetic quantum number is an integer that specifies the
orientation of the orbital


Values are integers from −l to +l


the direction in space the orbital is aligned relative to the other orbitals
including zero
Gives the number of orbitals of a particular shape
l = 2, the values of ml are −2, −1, 0, +1, +2; which means there are five orbitals
with l = 2
 when