Discussion
The magnitude of an earthquake is a measure of the energy released during the earthquake. The difference in energy released between an earthquake of magnitude 4 and one of magnitude 7 on the Richter scale is about :
Answer: C
The difference is about 27,000 times.
Energy released rises by a factor of about \(10^{1.5} \approx 31.6\) for each whole unit of magnitude, from \(\log E = 1.5M + \text{constant}\). A difference of 3 units gives:
\[ \begin{aligned} \frac{E_{7}}{E_{4}} &= 10^{1.5 \times 3} = 10^{4.5} \\ &\approx 31{,}600 \end{aligned} \]
Using the rounded factor of 30 per unit, as textbooks often do, gives \(30^{3} = 27{,}000\), the option offered. 30 times is the factor for one unit only, and 900 times for two. 3,000 is not a power of the factor at all. Ground-motion amplitude, not energy, rises by 10 per unit, which would give 1,000.
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