The 1933 earthquake in Japan registered 8.9 on the Richter scale.
a.The 1985 earthquake in Peru registered 7.7 on the Richter scale. How many more times intense was the earthquake in Japan? Round your answer to one decimal place.
b. What would the Richter scale reading be of an earthquake that is only 0.01 times as intense as the earthquake in Japan?
6.9 and 0.01
a. To determine how many more times intense the earthquake in Japan was compared to the earthquake in Peru, we need to calculate the difference in magnitude on the Richter scale.
The magnitude difference (Md) can be calculated using the formula:
Md = log10(I1/I2)
Where I1 is the intensity of the earthquake in Japan and I2 is the intensity of the earthquake in Peru.
First, we need to convert the magnitude on the Richter scale to intensity. The relationship between magnitude and intensity is as follows:
I = 10^(1.5 * M + 4.8)
Where I is the intensity and M is the magnitude.
For the earthquake in Japan, M1 = 8.9. Thus, the intensity of the earthquake in Japan (I1) can be calculated as:
I1 = 10^(1.5 * 8.9 + 4.8)
For the earthquake in Peru, M2 = 7.7. Thus, the intensity of the earthquake in Peru (I2) can be calculated as:
I2 = 10^(1.5 * 7.7 + 4.8)
Now, we can calculate the magnitude difference:
Md = log10(I1/I2)
Finally, round the answer to one decimal place.
b. To determine the Richter scale reading of an earthquake that is only 0.01 times as intense as the earthquake in Japan, we need to solve for the magnitude using the formula:
I = 10^(1.5 * M + 4.8)
First, let's assume the intensity of the earthquake in Japan (I1) is known. We can then find the intensity of the less intense earthquake (I2) using the relationship:
I2 = 0.01 * I1
Then, we can rearrange the formula and solve for the magnitude (M):
M = (log10(I2) - 4.8) / 1.5
Plug in the known values to calculate the magnitude on the Richter scale.