A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.4 multiplied by 102 µm. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth.)
To find the earthquake's magnitude on the Richter scale, we can use the formula:
M = log10(A) + 3*log10(D) - 2.92
Where:
M = magnitude on the Richter scale
A = maximum amplitude of the seismograph reading in millimeters
D = distance from the epicenter of the earthquake in kilometers
First, let's convert the maximum amplitude from micrometers to millimeters:
5.4 * 10^2 µm = 5.4 * 10^-1 mm
Next, we can substitute the values into the formula. Given that the amplitude is 5.4 * 10^-1 mm and the distance is 300 km, we have:
M = log10(5.4 * 10^-1) + 3*log10(300) - 2.92
Calculating the logarithms:
M = log10(0.54) + 3 * log10(300) - 2.92
Using a calculator:
M ≈ -0.268 + 3 * 2.477 - 2.92
M ≈ -0.268 + 7.431 - 2.92
M ≈ 4.243
Therefore, the earthquake's magnitude on the Richter scale is approximately 4.2 (rounded to the nearest tenth).