Question

On the Richter scale, the magnitude, M, of an earthquake is given by M= 2/3logE/Eo, where E is the energy released by the earthquake measured in joules, and Eo is the energy released by a very small reference earthquake. Eo has been standardized to 10^4.4 joules.

Part A
The earthquake in Haiti in 2010 released 2.0*10^15 joules. What was its magnitude on the Richter scale?

Part B
If the energy release of one earthquake is 10,000 times that of another, how much larger is the Richter scale reading of the larger earthquake than the smaller?

Answer 1

A ; M = 7.267

B ; M = 2.667

Explanation:

Formula

M = (2/3) log (E/Eo)

M = 2/3 * log (2 * 10^15/10^(4.4) )

M = 2/3 * log( 7.9621* 10^10)

M = 2/3 * 10.901

M = 7.267 on the Richter scale.

Part B

Suppose that you use Eo and your base. Eo is 10^4.4

Now the new earthquake is E = 10000 * Eo

So what you get now is M = (2/3)* Log(10000 * Eo / Eo )

M = 2/3 * log(10000)

M = 2/3 of 4

M = 8/3

M = 2.6667

What this tells you is that if the original reading was (say) 6 then the 10000 times bigger reading would 8.266667

Answer 2

See below

Explanation:

Part A

Formula

M = 2/3 * log(E/Eo)

Givens

M = ??

E = 2 * 10^15 joules

Eo = 10^4.4

Solution

M = (2/3) * log(2 * 10^15 / 10^4.4)

M = (2/3 ) log (7.96 * 10 ^ 11)

M = (2/3) * 11.901

M = 7.934

Part B

What the question is saying is that E/Eo = 10000

You don't have to figure out exact values.

M = 2/3 * log(10000)

M = 2/3 * 4

M = 8/3 or 2 2/3 or 2.66667

If you have choices, please list them.