9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:11:56 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Alex H. Yuan - 09/06/2014 4:11:56 PM EDT
General Chemistry (First Semester) / Chem 110 FA 2014 – CH110 FA14 S25-36 (Dr.
Barber)
1.
Interconverting wavelength, frequency and photon energy
It takes
to break an iodine-iodine single bond. Calculate the maximum
wavelength of light for which an iodine-iodine single bond could be broken by absorbing
a single photon.
Be sure your answer has the correct number of significant digits.
You can answer this question by using the fact that the frequency and photon energy of
electromagnetic radiation are related through this equation:
In this equation stands for the energy of each photon of the radiation,
frequency of the radiation, and is the Planck constant.
stands for the
First, rearrange the equation to solve for so you can calculate the minimum frequency of
light needed to break an iodine-iodine single bond:
Here's the rearranged equation.
You might be tempted to substitute
for in this equation. But that would be
wrong. That's because
is the energy required to break a mole of bonds,
while stands for the energy needed to break just one.
To calculate the energy required to break just one bond, divide
Avogadro constant:
There are
significant digits in
by the
That means your calculated value for
has
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9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:11:56 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
only significant digits. But keep two extra digits for now, and only round your final answer
to the correct number of significant digits.
Now you can use the rearranged equation:
Substitute your calculated value for
value of the Planck constant for
and the
Cancel units, and use the calculator to divide
the numbers.
There were
significant digits in your calculated value for
so your calculated value for
has significant digits. But keep two extra digits for now, because you have one more
calculation to make.
Finally, you need to calculate the wavelength of light that corresponds to this frequency.
Use the relationship between frequency and wavelength and the speed of light:
In this equation
stands for wavelength, and
stands for the speed of light.
Substitute the speed of light for
and your
calculated value of the frequency for
Cancel units, and use the calculator to divide the
numbers.
Since the speed of light is an exact number, and your calculated value for the frequency
had significant digits, your calculated value for the wavelength has significant digits.
Be sure you round your final answer correctly.
Also, a scientist would usually convert
nanometers.
to a more convenient unit, like
The maximum wavelength of light is
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9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:11:56 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Copyright © 2014 UC Regents and ALEKS Corporation
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