Question

Seismologists use the Richter scale to express the energy, or magnitude, of an earthquake. The Richter magnitude of an earthquake, M, is related

energy released in ergs E shown by the formula
M
flog (10)
A recent earthquake in Peru registered a 4.0 on the Richter scale. How much energy in ergs was released by this earthquake?
(Enter you answer in terms of 10 and use Shift 6^ for exponents)
ergs

Answer 1

10¹⁸ ergs

Explanation:

From the question,

Using the expression

M =
`(4)/(5)`log(E/10¹³)................. Equation 1

Where M = Richter magnitude of earth quake, E = Energy released in ergs.

Given: M = 4.0

Substitute into equation 1 amd solve for E

4 =
`(4)/(5)`log(E/10¹³)

Log(E/10¹³) = (4×5)/4

Log(E/10¹³) = 5

E/10¹³ = 10⁵

E = 10⁵×10¹³

E = 10⁵⁺¹³

E = 10¹⁸ ergs