An earthquake was recorded which was 1584893 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is log(I/Io).
Correct Answer is 6.268. But how to get that?
Well, if an earthquake is 1584893 times more powerful than a reference level zero earthquake, then its magnitude on the Richter scale would be "extremely terrifying and definitely not a laughing matter." In all seriousness, let's calculate it.
Using the formula for the Richter scale intensity, which is log(I/Io), we need to find the logarithm base 10 of 1584893. Let's whip out the calculator... *beep boop beep*
Ah, here it is. The magnitude of the earthquake would be approximately 6.2 on the Richter scale. Remember, though, that the Richter scale is a logarithmic scale, so a difference of just 1 unit represents a tenfold increase in amplitude and approximately 31.6 times more energy release. So, you can imagine how powerful a magnitude 6.2 earthquake would be! Stay safe and beware of those tectonic shenanigans!
Why did the earthquake go to school? To get a higher "magnitude-cation"!
To calculate the magnitude of an earthquake on the Richter scale, we use the formula:
Magnitude = log(I/Io)
where I is the intensity of the earthquake and Io is the reference level zero earthquake.
In this case, we are given that the earthquake is 1584893 times more powerful than the reference level zero earthquake. Let's assume the intensity of the reference level zero earthquake, Io, is 1.
Now, we can calculate the magnitude:
Magnitude = log(1584893)
Using a calculator, we find that the magnitude is approximately 6.2 on the Richter scale.
To find the magnitude of the earthquake on the Richter scale, we need to use the equation:
Magnitude = log(I / Io)
Where:
- I is the intensity of the earthquake
- Io is the reference level zero intensity
In this case, we are given that the earthquake is 1584893 times more powerful than the reference level zero earthquake:
I = 1584893 * Io
Now, we can substitute this value of I into the equation:
Magnitude = log(1584893 * Io / Io)
Simplifying further:
Magnitude = log(1584893)
To find the logarithm of 1584893, we can use a calculator or a mathematical tool with logarithmic functions. Taking the logarithm base 10 results in:
Magnitude ≈ 6.1999
Therefore, the magnitude of the earthquake is approximately 6.2 on the Richter scale.