9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:24:26 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Alex H. Yuan - 09/06/2014 4:24:26 PM EDT
General Chemistry (First Semester) / Chem 110 FA 2014 – CH110
FA14 S25-36 (Dr. Barber)
1.
Predicting the qualitative features of a line spectrum
This energy diagram shows the allowed energy levels of an electron in a certain
atom or molecule:
B
C
D
energy
E
Use this diagram to complete the table below.
Which is the ground state?
(pick one)
How many excited states are there?
How many lines are in the absorption line spectrum?
Which transition causes the absorption line at the shortest wavelength?
Which transition causes the absorption line at the longest wavelength?
You can solve this problem by using some important facts about
spectroscopy.
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9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:24:26 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
spectroscopy.
First, complete the top two rows of the table by using the fact that the
state with the lowest possible energy is called the ground state, and
all other states are called excited states.
That means the ground state in this problem is E, and there are
excited states.
Next, use the fact that there's a line in the absorption line spectrum of
a system for each possible transition that absorbs energy.
For example, for the energy level diagram shown in this
problem, there are transitions that start from the lowest state
and absorb energy (shown below at left), and transitions that
start from the next lowest state and absorb energy (shown
below at right):
B
B
C
C
D
D
energy
energy
E
E
Altogether, if you count carefully, there are
transitions that
absorb energy. That means there would be
absorption line spectrum of this system.
lines in the
On the other hand, there's a line in the emission line spectrum of a
system for each possible transition that releases energy.
For example, for the energy level diagram shown in this
problem, there are transitions that start from the highest state
and release energy (shown below at left), and transitions that
start from the next highest state and release energy (shown
below at right):
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9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:24:26 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
B
B
C
C
D
D
energy
energy
E
E
Altogether, if you count carefully, there are
release energy. That means there would be
emission line spectrum of this system.
transitions that
lines in the
Finally, to complete the last two rows of the column, use the
relationship between the energy of a photon and its frequency or
wavelength:
In this equation
the photon,
stands for the energy of
stands for its frequency, and
is the Planck constant.
You can derive this equation from the
previous line by using the fact that
where
stands for wavelength and
the speed of light.
is
The first equation tells you that the frequency of a line in the emission
or absorption line spectrum is directly proportional to the energy
released or absorbed by a transition. On the other hand, the second
equation tells you the wavelength of a line is inversely proportional to
the energy released or absorbed by a transition.
In other words, the line in the absorption or emission spectrum with
the longest wavelength will come from the transition that absorbs or
releases the least amount of energy.
For the energy level diagram shown in this problem, that would
be the transition between C and B.
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9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:24:26 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
be the transition between C and B.
On the other hand, the line in the absorption or emission spectrum
with the shortest wavelength will come from the transition that
absorbs or releases the most amount of energy.
For the energy level diagram shown in this problem, that would
be the transition between E and B.
Here is the completed table:
Which is the ground state?
E
How many excited states are there?
3
How many lines are in the absorption line spectrum?
6
Which transition causes the absorption line at the shortest wavelength?
E
B
Which transition causes the absorption line at the longest wavelength?
C
B
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