The intensity of an earthquake of magnitude 8 on the Richter scale is greater than the intensity of an earthquake of magnitude 5 on the same scale by ________ times.
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Correct Answer: 1000
Solution and Explanation
The Richter scale is logarithmic. This means that each increase of 1 unit on the scale corresponds to a tenfold increase in the amplitude of the earthquake. Additionally, the intensity of an earthquake is proportional to the square of the amplitude. Therefore, the intensity of an earthquake increases by a factor of 100 for each unit increase in magnitude.
Step 2: Calculation of Intensity Ratio.
For magnitude 8 and 5, the difference in magnitude is \(8 - 5 = 3\). Using the formula for the intensity ratio based on the Richter scale: \[ \text{Intensity Ratio} = 10^{(3 \times 2)} = 10^{6} = 1000 \, \text{times}. \] Step 3: Conclusion.
The intensity of an earthquake of magnitude 8 is 1000 times greater than the intensity of an earthquake of magnitude 5.
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