A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.2 102 µm. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth.)
M =
To find the magnitude of an earthquake on the Richter scale, we can use the formula:
M = log10(A) + 3log10(D) - 2.92
Where:
M is the magnitude on the Richter scale
A is the maximum amplitude recorded by the seismograph
D is the distance from the epicenter to the seismograph in kilometers
In this case, the maximum amplitude (A) is given as 5.2 * 10^2 µm, and the distance (D) is 300 km.
First, let's convert the amplitude from micrometers to meters. We know that 1 meter is equal to 1 million micrometers (µm), so we divide the amplitude by 1 million:
A = (5.2 * 10^2) / 10^6 = 5.2 * 10^(-4) meters
Now we can substitute the values into the formula:
M = log10(5.2 * 10^(-4)) + 3log10(300) - 2.92
Next, calculate the logarithms using a calculator:
log10(5.2 * 10^(-4)) ≈ -3.28
log10(300) ≈ 2.48
Substitute the values into the formula:
M = -3.28 + 3 * 2.48 - 2.92
Simplify the expression:
M = -3.28 + 7.44 - 2.92
M = 1.24
Therefore, the magnitude of the earthquake on the Richter scale is approximately 1.2.