Chapter 2.3, Problem 65E

Richter Scale The Richter scale is used to measure the intensity of earthquakes. The Richter scale rating of an earthquake is given by the formula

$R=\frac{2}{3}\left(\log E-11.8\right)$ where E is the energy released by the earthquake (measured in ergs⁴²).

a. The San Francisco earthquake of 1906 is estimated to have registered $R=7.9$ on the Richter scale. How many ergs of energy were released?

b. The Japan earthquake of 2011 registered 9.0 on the Richter scale. Compare the two: The energy released in the 1906 earthquake was what percentage of the energy released in the 2011 quake?

c. Solve the equation given above for E in terms of R.

d. Use the result of part (c) to show that if two earthquakes registering $R_1$ and $R_2$ on the Richter scale release $E_1$ and $E_2$ ergs of energy, respectively, the

$\frac{E_2}{E_1}={10}^{1.5}\left(R_2-R_1\right)$

e. Fill in the blank: If one earthquake registers 2 points more on the Richter scale than another, then it releases __________times the amount of energy.