The Richter Scale (Click here to a MSWord version of this page.)
A scale for comparing the intensities of earthquakes was devised
around 1940, by a man named Charles Richter. The intensity of an earthquake is
measured by the amount of ground motion as measured on a seismometer. The
Richter scale is not designed so that you must know the actual intensities or
seismometer readings. The scale is simply used to compare intensities according
to the following rule:
Each increase of 1 unit in
magnitude on the Richter scale corresponds to a 10-fold increase in intensity as
measured on a seismometer.
This makes it relatively easy to
compare the intensities of earthquakes with a magnitude difference of integer
amounts. For example, the 1976 Italy earthquake was a magnitude of 6.5, while
the Guatemala earthquake of the same year had a magnitude of 7.5, which is
exactly one unit greater. This means the second earthquake was 10 times more
intense than the first.
1) |
Calculate, using exponents, the intensity difference between a 5.5 magnitude quake and a 7.5. |
2) | Calculate, using exponents, the intensity difference between a 5.5 and an 8.5. |
How do we compare the intensities of earthquakes that do not differ by a whole number?
We can do this by using a property of exponents. If we express the intensity I as an exponential function of the magnitude M.
We will use the Alaska and Turkey earthquakes of 1964 and 1966.
This represents the Alaska earthquake. And this is the Turkey earthquake. We are asked to compare intensities, so the ratio will be useful. =39.81 =approximately 40 times as intense. |
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We can
also use exponents to calculate the energy of an earthquake. The formula for the
energy (in kWh, kiloWatt hours) is:
where E is the energy, and M is
the earthquake magnitude.
5) |
Calculate the energy of a magnitude 8.7 earthquake. |
6) | Calculate the energy of a magnitude 9.0 earthquake. |
7) | Using your results from above, can you calculate how many years you would have to run a 100W lightbulb to use the same amount of energy as in the 9.0 quake? |
Now that you understand the Richter scale, let's try to discover what effect the large earthquake will have on Vancouver.
See solutions to the questions. |
Back to Earthquake Math Trail Home |