Use the formula . In October 2004, an earthquake measuring 6.8 on the Richter scale occurred in Japan. The largest quake in Japan since 1990was one in 1993that registered 7.7. How many times more severe was the 1993shock than the one in 2004on the Richter scale? Round your answer to one decimal place.

A)0.8 times as severe
B)6.1 times as severe
C)7.9 times as severe
D)8.5 times as severe
E)17.1 times as severe

Question

Use the formula  . In October 2004, an earthquake measuring 6.8 on the Richter scale occurred in Japan. The largest quake in Japan since 1990was one in 1993that registered 7.7. How many times more severe was the 1993shock than the one in 2004on the Richter scale? Round your answer to one decimal place.
​
A)0.8 times as severe 
B)6.1 times as severe 
C)7.9 times as severe 
D)8.5 times as severe 
E)17.1 times as severe

Quizplus · Accepted Answer

The formula to calculate the ratio of two earthquakes based on their magnitude on the Richter scale is:

log(Mb/Ma) = (1/3) × log(Eb/Ea)

where Mb and Ma are the magnitudes of the two earthquakes and Eb and Ea are the energies released by them.

Using the given formula 11eb0d3b_9818_4145_9790_973788a94bfe_TB1243_11, we can calculate:

log(7.7/6.8) = (1/3) × log(Eb/Ea)

Solving for Eb/Ea, we get:

Eb/Ea = (10^(log(7.7/6.8) / (1/3))) = 7.943

Therefore, the 1993 quake was 7.9 times more severe than the 2004 quake on the Richter scale. The answer is C.

Use the Formula