Question 1186916: Supposed that an earthquake released 10^6 joules of energy.What is the magnitude on a richr scale?How much more energy released that the reference earthquake?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Calculate the Richter scale magnitude:**
The formula relating energy released (E) to Richter scale magnitude (M) is:
log₁₀(E) = 4.4 + 1.5M
Where:
* E is the energy released in joules
* M is the Richter scale magnitude
Plug in the given energy (E = 10⁶ joules) and solve for M:
log₁₀(10⁶) = 4.4 + 1.5M
6 = 4.4 + 1.5M
1.6 = 1.5M
M = 1.6 / 1.5
M ≈ 1.07
Therefore, an earthquake releasing 10⁶ joules of energy has a magnitude of approximately **1.07** on the Richter scale.
**2. Calculate the energy released relative to the reference earthquake:**
The Richter scale is a logarithmic scale. Each whole number increase in magnitude represents a tenfold increase in amplitude and approximately 31.6 times more energy released.
The reference earthquake for the Richter scale is assigned a magnitude of 0. Let E₀ be the energy released by the reference earthquake.
Using the formula:
log₁₀(E₀) = 4.4 + 1.5 * 0
log₁₀(E₀) = 4.4
E₀ = 10⁴.⁴ joules
To find how much more energy the given earthquake released compared to the reference earthquake, we can divide the energy released by the given earthquake by the energy released by the reference earthquake:
Energy ratio = E / E₀ = 10⁶ / 10⁴.⁴ = 10¹·⁶ ≈ 39.81
Therefore, the earthquake released approximately **39.81 times** more energy than the reference earthquake.
|
|
|
