What is the magnitude on the Richter Scale of an earthquake measuring
3.7 x 10^5 i(sub 0)?
How many times more intense is a Richter 5 earthquake than a Richter 2.5 earthquake?
To determine the magnitude on the Richter Scale of an earthquake measuring 3.7 x 10^5 i₀, we need to understand how the Richter Scale works. The Richter Scale is a logarithmic scale used to quantify the energy released by an earthquake.
To calculate the magnitude on the Richter Scale, we need the value of i₀, which represents the amplitude of seismic waves measured by a seismograph. The formula to calculate the magnitude on the Richter Scale is as follows:
Magnitude (M) = log10(i₀) + 3
Where i₀ is the maximum amplitude in micrometers recorded on the seismograph during the earthquake.
In this case, the value of i₀ is given as 3.7 x 10^5. To calculate the magnitude, we substitute this value into the formula:
Magnitude (M) = log10(3.7 x 10^5) + 3
Using logarithmic properties, we can simplify this:
Magnitude (M) = log10(3.7) + log10(10^5) + 3
Magnitude (M) = 0.568 + 5 + 3
Magnitude (M) = 8.568
Therefore, the magnitude on the Richter Scale for an earthquake measuring 3.7 x 10^5 i₀ is approximately 8.568.
To determine how many times more intense a Richter 5 earthquake is compared to a Richter 2.5 earthquake, we need to utilize the logarithmic nature of the Richter Scale.
The Richter Scale is logarithmic, meaning that each whole number increase on the scale corresponds to a tenfold increase in the amplitude of the seismic waves and approximately 31.6 times more energy released.
The difference in magnitude between a Richter 5 earthquake and a Richter 2.5 earthquake is 5 - 2.5 = 2.5.
To calculate the difference in intensity, we can use the following formula:
Intensity difference = 10^(1.5 * magnitude difference)
In this case, the magnitude difference is 2.5, so we calculate:
Intensity difference = 10^(1.5 * 2.5)
Intensity difference = 10^(3.75)
Taking 10 to the power of 3.75, we get approximately 5623.413.
Therefore, a Richter 5 earthquake is approximately 5623 times more intense than a Richter 2.5 earthquake.