U of Arizona
Midterm 2 Study Guide UNIT2: How do we determine structure?
M1: Analyzing Light-Matter Interactions
1. Analytical methods based on the analysis of different types of EM radiation absorbed or
emitted by chemical substances.
2. EM radiation: form of energy that can be generated by accelerating particles that have an
3. The figure below is a representation of an EM wave with its basic components: Electric field E
and magnetic field B that oscillate in phase perpendicular to each other and perpendicular to
the propagation direction k. this wave is characterized by its wavelength lambda- a measure of
the distance over which the shape of the wave is repeated; the frequency v indicates the
number of repeating waves that cross a certain point of space per unit time.
The relationship between wavelength
λ, frequency v, and speed of propagation v of a wave has the relationship: λ*v=v
If EM wave is travelling through vacuum, speed of propagation has a constant value of
The figure below shows the EM spectrum with visible range of spectrum zoomed in. Spectroscopy techniques all use a detector to measure the intensity of the EM radiation that
passes through a sample or is emitted by a substance when heated or stimulated. Eg. A typical
absorption spectrometer includes a EM radiation source, a device to spilt the radiation into
specific wavelengths, and a detector.
What information can be obtained by analyzing a chemical substance using absorption
Information about absorbance or the fraction of EM radiation of a specific wavelength that was
absorbed by the substance or the fraction of that EM radiation that went through the sample
without being absorbed (transmittance).
Max Planck's experiments to explain how the intensity of EM radiation generated by an object
depends on the frequency of the radiation and the temperature of the object had these two
1. The energy transferred E through light-matter interactions is proportional to the frequency v of
the EM radiation according to:
E=h*v where h=6.626*10 J, h is called Planck's constant
2. Energy transfer during light-matter interactions only occurs in integer multiples of the
elementary unit of energy: E=h*v
This means energy transfer in light-matter interactions is quantized: it can only take a set of discrete
values instead of any possible value.
Based on Planck's model, Einstein proposed that EM radiation was composed of discrete
quanta of energy called photons. According to this model, electrons are ejected by direct
interaction with those photons with an energy E = hv above the threshold value, and the larger
the frequency of the photon, the larger the amount of energy transmitted to the charged
This model implies that quantization is an intrinsic property of light.
Use the following formulas and table to answer the questions
E = hv C= λv
E is the energy of the light in Joules (J),
h is a constant which is 6.626 X 10 J·s, and
v is the frequency of the light in s or waves/s (also called Hertz (Hz).
C is the speed of light. C = 3.00 X 10 meters/sec.
λ is the wavelength
(There are 1 X10 nanometers in one meter.)
-1 14 14 14 14 14 14
Frequency, s or (1/s) 7.1 X 10 6.4 X 10 5.7 X 10 5.2 X 10 4.8 X 10 4.3 X 10
Color violet blue green yellow orange red -19
1. A photon of light with an energy of 2.2 X 10 Joules is emitted. What is the frequency of
this photon? What color is it?
1. 3.3 X 10 Hz, infrared
2. What is the wavelength, in nanometers, of light with a frequency of 7.1 X 10 Hz?14
2. 420 nm, violet
The figure below shows the emission and absorption spectra of hydrogen in the visible range.
Note that the absorption and emission lines have the same wavelength. Why?
The energy of electrons in atoms is also quantized. In order for an atom to change its energy level, it
needs to absorb or release a photon with an energy equal to the difference between two existing energy
levels. Thus, the location of the absorption or emission lines gives information about the allowed energy
levels for electrons of atoms.
See figure below where different lines the absorption or emission spectra of atoms correspond to
electron transitions between different energy levels.
From the figure above, if we assign a label n=1,2,… to each allowed energy level, the energy of each
level can be represented by Ei. The absolute difference between any two levels should then satisfy the relationship:
Where v is the frequency of a single photon
If one mole of atoms absorb or emit a photon with energy Hv, the total energy absorbed or released
Et will be as follows:
The electrons in most atoms tend to occupy the lowest energy levels at standard conditions of
temperature and pressure (ground state)
When heated, electrons may move to higher levels by absorbing energy (excited state).
Bohr's Atomic Model was the first to qualitatively explain the quantized nature of light
absorption by matter and to qualitatively predict the actual wavelength of the absorption lines.
Bohr proposed that the energy of electrons in atoms was quantized.
De Broglis and Schrodinger Atomic Models take a wave not discrete particle view of electrons in
atoms. This means (in particular for Schrodinger's model) we can only predict the probability of
finding electrons in certain regions of space.
Quantum Mechanical Model
Atoms can exist in different electronic energy states depending on how their electrons are
distributed among various energy levels. The energy difference between energy levels can be
deduced from spectroscopic data.
1. If the absorption of light with wavelength 122nm induces an electron transition
from the ground state with n=1 to the excited state with n=2 in the hydrogen
atom then, what is the energy needed to promote one electron from n=1 to
2. What is the total energy required to induce this change in one mole of hydrogen
atoms? Electrons can be absorbed enough energy to detach from the atom and form ions in case of
high energy EM radiation like UV, X-ray, or gamma ray.
In quantum mechanical model of atom, energy quantization is seen as a direct result of the
intrinsic properties of subatomic particles. The model assumes that electrons in confined
systems, such as atoms or molecules, behave like stationary waves. These waves occur only in a
discrete set of wavelengths or frequencies. The consequence is discrete electronic states.
Figure below shows how a 2D surface can only vibrate in certain modes (explains modern
model of atom)
If energy is associated with the frequency of each allowed standing wave, like photons, then
quantization of energy is natural due to wavelike behavior of electrons. Mass, number of
electrons, strength of interactions between electrons and protons in an atom all determine the
quantized states in an atom.
Heisenburg's principle: there is a fundamental limit to the precision with which certain pairs of
physical properties of a particle, known as complementary variables, such as position x and
momentum p, can be known.
Therefore, we cannot determine precise trajectories of electrons because we do not have
precise knowledge of their position and velocity as a function of time (momentum). The most we can determine is the probability of finding electrons in certain region of the space
at a given time.
Probability density p of an electron confined inside a flat surface is shown in the figure below.
The more localized an electron is, the larger its kinetic energy. Thus, delocalization, or
redistribution of electrons in a larger space, reduces their kinetic energy.
Electrons with different energies are described by different wave functions. In particular, their kinetic
energy is directly related to the wavelength of their assorted wave function. The smaller the
wavelength, the higher the kinetic energy. For electrons forced to move closer to nucleus., the kinetic
energy will be higher than those farther away from nucleus.
Molecules exist in quantized electronic states but also vibrational and rotational energy states.
The figure below shows the energy scale for different types of molecular transitions UV and visible radiation tends to induce electronic excitations resulting in bond breaking and atom
separation. The energy differences between electronic levels of molecules are in the order of 10^2 to
IR radiation of lower frequency and thus lower energy, stimulates transitions between different
vibrational states. The energy differences between these levels are in the order of 10^-1 to 10^-2
Microwave radiation induces molecular transitions between different rotational states. The energy
differences between these levels are in the order of 10^-3 to 10^-1 kJ/mol
Wavenumber: defined as inverse of wavelength; commonly used to represent data in IR
1. What is the significance of determining energy difference to induce molecular
This is useful in predicting changes that substances may undergo when exposed to different energy
2. If vibrational energy states are quantized, why do we observe absorption over a range of
frequencies rather than at single peaks?
2. The existence of broad absorption bands in molecular compounds is due to the multiple interactions
between atoms in the same molecule and between different molecules in the system. Molecular rearrangements introduce tiny changes in vibrational and rotational energy levels so
that molecules of the same subtance have small variations in absorption frequencies. Low
resolution spectroscopes may not detect these variations and show a continuous frequency
range instead of a clearly quantized peaks of high-resolution machines.
Aura Mission NASA: Different types of spectroscopic measurements permit detection of several
chemical species at different altitudes in the atmosphere. Follow the evolution of 20 diff
chemical substances over time across the planet.
Atomic Absorption spectroscopy
Used to detect trace amounts of metals in food and environmental samples, drugs (metals may
be used in drug synthesis and their final concentration may be monitored in the final product),
mining raw materials ( to determine toxic impurities like lead, determine concentration of metal
in ore), clinical labs (determine change in metal concentration in pathologies)
Sample is vaporized and atomized as high as 3000 degree C. the energy provided is enough to
break chemical bonds within sample and produce free ground-state atoms or ions. A radiation
source with the same metal as the one being detected is also present.
The metal is excited to generate EM radiation characteristic of its emission spectrum, which is
passed through the vaporized sample. If the metal of interest in present, it will absorb the
incoming EM radiation. The amount of radiation absorbed will be proportional to the metal's
Stars emit EM radiation in a continuous range of wavelengths. But the intensity at each specific
wavelength is a function of temperature. THE EM spectrum of a star can be modeled by
assuming it behaves as perfect radiation emitter or absorber (blackbody object).
Chemical elements in a star's photosphere absorb specific radiation. The dips in their spectra as
measured at the top of our planet's atmosphere can be used to detect their presence in the star.
The shape of the spectra is indicative of the star's temperature.
Our sun's EM spectrum as measured from earth is similar to that of star with a surface
temperature of 5500C. However, its fine structure depends on the altitude where it is
measured. The figure below show the absorption spectrum of liquid water
M2: Looking for Patterns
Electrostatic model: When two atoms are in close proximity, electrostatic interactions between
electrons and protons of the atoms form a net attractive force between the atoms. As atoms get closer, strength of attractive interaction increases until reaching a point in which repulsive
interactions between charges of same type of begin to dominate.
The bond length is defined as the distance at which the average electron-electron and proton-proton
repulsive forces (red) and balanced by the average electron-proton attractive forces (black). See
The bond between two neutral atoms that results from this dynamic interaction between
electrons and protons in the system is called a covalent bond
In the electrostatic model of covalent bonding, the formation of a bond between two atoms
alters the energy of the system.
Interactions between protons of one atom and electrons of another such that some electrons
are pulled to the space between the atoms. These electrons have high potential but low
Other electrons take up the space vacated by these electrons and move closer to the nucleus,
decreasing their potential.
If atoms get too close, repulsion between like charges increases both kinetic and potential
energy of interacting particles.
There is an optimal bond length at which the energy of the system is minimum.
In the quantum model of covalent bonding, bonds is seen by looking at the electron density
of participating atoms.
Bond formation allows for electron delocalization i.e. allows some electrons to occupy a
larger region in space, which decreases their kinetic energy.
Covalent bonding is driven by the delocalization of electronic motion between the two
bonded atoms which causes a redistribution of electron density in the entire system.
What is the similarity between electrostatic and quantum model of covalent bonding?
ANSWER: In the quantum model, as some electrons delocalize into the bonding region, the remaining
electrons in each atom can get closer to their atomic nuclei which lowers their potential energy. This
is also seen in the electrostatic model. Bonding Patterns
Atoms in a molecule vibrate around their equilibrium position at frequencies determine by the
molecule's atomic composition and connectivity. The vibrational states are quantized and different
molecules will undergo vibrational transition at characteristic frequencies when interacting with EM
radiation. The following is an IR (infrared) absorption spectrum of formaldahyde (CH2O)
Specific bonding arrangements exhibit characteristic vibrations (bending, stretching) that can be
excited at specific frequencies or wavenumbers.
Stable covalent bonds are formed when atleast 2 electrons are delocalized between the bonded
atoms (forming a single bond). Double and triple bonds involve four and six delocalized electrons
The present of these different bonds can change bond strength, thus affecting the energy of the
vibrational states allowed in the system.
IR absorption bands appear at highest wavenumbers for triple bonds, followed by double and
then single bonds. i.e. more energy is needed to generate equivalent vibrational transitions
involving stronger bonds and bonds between lighter atoms which vibrate at higher frequencies.
IR spectroscopic data may not tell us the number of each type of bond in a molecule but it does
tell us about the molecular structure of a compound.
Stretching and bending are most common molecular vibrations.
Atoms have a fixed bonding capacity (valence) independent of the nature of the atoms
to which they are connected.
Molecular compounds can result from the combination of atoms of non-metallic
Periodic properties: atomic properties that vary regularly across a group (column) or a
period (row) in the Periodic Table. These properties allow us to predict the physical and
chemical properties of substances. QUESTION
What are some examples of elements that tend to deviate from the periodic trend?
Atoms with larger number of electrons in any given group like Sulfur, Phosphorus, etc. tend to deviate
from the trend.
Electronic configurations: how electrons distribute in both space and energy levels within atoms.
If we define bond length (d) as the distance between the atomic nuclei of two bonded atoms, we can
assume that this distance should have a value close to the result of adding the atomic radius (r ) of
the atoms. Thus, by measuring the length of bonds between similar and different types of atoms in
many molecules, we can start building a scale of atomic sizes based average values.
Atomic size of neutral atoms decreases as the atomic number Z increases within a period and it
increases as the atomic number increase within a group.
First Ionization Energy E1: the minimum energy needed to remove an electron from the neutral
atoms of an element in gaseous state.
The first ionization energy increases as we move from bottom to top within a group and from