The magnitude M of an earthquake is given.
a. Find the earthquake intensity I in terms of the​ zero-level earthquake intensity Upper I 0.
b. Find the energy released by the earthquake.
Mequals2


Given that the magnitude \( M \) of an earthquake is \( 2 \), we can solve the following:

### Part (a): Find the earthquake intensity \( I \) in terms of the zero-level earthquake intensity \( I_0 \).

The Richter scale defines the earthquake magnitude \( M \) in terms of the ratio of the earthquake intensity \( I \) to a reference intensity \( I_0 \) by the following logarithmic equation:

\[
M = \log_{10} \left( \frac{I}{I_0} \right)
\]

For \( M = 2 \), the equation becomes:

\[
2 = \log_{10} \left( \frac{I}{I_0} \right)
\]

To solve for \( I \), we first rewrite the equation in exponential form:

\[
\frac{I}{I_0} = 10^2
\]

\[
I = I_0 \cdot 10^2 = I_0 \cdot 100
\]

Thus, the intensity \( I \) is:

\[
I = 100 \cdot I_0
\]

### Part (b): Find the energy released by the earthquake.

The energy \( E \) released by an earthquake can be related to the magnitude \( M \) by the equation:

\[
E = E_0 \cdot 10^{1.5M}
\]

where \( E_0 \) is a constant reference energy. For \( M = 2 \):

\[
E = E_0 \cdot 10^{1.5 \times 2} = E_0 \cdot 10^3
\]

Thus, the energy released by the earthquake is:

\[
E = 1000 \cdot E_0
\]

In summary:
- The intensity \( I = 100 \cdot I_0 \).
- The energy released \( E = 1000 \cdot E_0 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the significance of the zero-level intensity \( I_0 \)?
2. How does the energy released by an earthquake scale with its magnitude?
3. What are the physical units of earthquake intensity \( I \)?
4. How would the intensity change if the magnitude \( M \) were 3 instead of 2?
5. Can the Richter scale be used to measure all types of seismic events?

**Tip:** The Richter scale is logarithmic, so each unit increase in magnitude corresponds to a tenfold increase in intensity and about 31.6 times more energy released.

The magnitude M of an earthquake is given. a. Find the earthquake intensity I in terms of the zero-level earthquake intensity I_0. b. Find the energy released by the earthquake. Mequals2

Explore how to calculate the earthquake intensity and the energy released for a magnitude 2 earthquake using the Richter scale. Understand the key logarithmic and exponential formulas involved in earthquake measurements. Suitable for Grades 10-12.

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