9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:30:25 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Alex H. Yuan - 09/06/2014 4:30:25 PM EDT
General Chemistry (First Semester) / Chem 110 FA 2014 – CH110 FA14 S25-36 (Dr.
Barber)
1.
Calculating the wavelength of a line in the spectrum of hydrogen
The energy
formula:
of the electron in a hydrogen atom can be calculated from the Bohr
In this equation
stands for the Rydberg energy, and
stands for the principal
quantum number of the orbital that holds the electron. (You can find the value of the
Rydberg energy using the Data button on the ALEKS toolbar.)
Calculate the wavelength of the line in the emission line spectrum of hydrogen caused
by the transition of the electron from an orbital with
to an orbital with
Round your answer to significant digits.
You can solve this problem by using a key fact about spectroscopy: when a system makes
a transition from one state to another, it emits or absorbs a photon with energy equal to the
difference in energy between the states.
That means, in this case, that the energy of the photon emitted when the electron goes
from the
orbital to the
orbital must equal the difference in energy between
these orbitals. Use the Bohr formula to calculate that difference:
Subtract the lower
energy from the
higher energy. The
orbital with larger
has the higher
energy.
Use the Bohr
formula for each
energy.
Substitute the value
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9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:30:25 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
of the Rydberg
energy for
Use the calculator
to multiply and
divide. You're going
to round your final
answer to 3
significant digits,
but keep two extra
digits until you're
done calculating.
Now you know the energy of the photon. Use the relationship between photon energy and
wavelength to calculate its wavelength:
In this equation stands for
the photon energy and
for
the wavelength, is the
Planck constant and is the
speed of light.
Rearrange the equation so
you can use it to calculate
from
Substitute your calculated
value of the photon energy
for Use the values for
and from the calculator, or
look them up using the Data
button on the ALEKS toolbar.
Cancel units, and use the
calculator to multiply and
divide numbers.
Convert to a more convenient
unit and round to 3 significant
digits.
The wavelength of the
emission line is
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9/6/2014
ALEKS Alex H. Yuan - 09/06/2014 4:30:25 PM EDT - Copyright © 2014 UC Regents and ALEKS Corporation
Copyright © 2014 UC Regents and ALEKS Corporation
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