A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.3 102 µm. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth.)
To find the magnitude of an earthquake on the Richter scale, you can use the formula:
Magnitude = log10(A/A0)
Where A is the maximum amplitude recorded by the seismograph (5.3 * 10^2 µm) and A0 is a reference amplitude (usually 1 µm).
First, let's convert the amplitude from micrometers to meters. Since 1 meter is equal to 1,000,000 micrometers, we have:
A = 5.3 * 10^2 µm = 5.3 * 10^2 * (1/1,000,000) = 5.3 * 10^2 / 10^6 m = 5.3 * 10^(-4) m
Now we have the amplitude in meters. Let's calculate the magnitude:
Magnitude = log10(A/A0) = log10(5.3 * 10^(-4) / 1)
To find the magnitude, we need to evaluate this logarithm. Using a calculator, we find:
Magnitude ≈ -3.8
Therefore, the magnitude of the earthquake on the Richter scale is approximately -3.8.