On the Richter scale the magnitude R of an earthquake is giv

On the Richter scale, the magnitude R of an earthquake is given by the formula R = log I/I_0 where I is the intensity of the earthquake being measured and I_0 is the standard reference intensity. Express the intensity/of an earthquake of magnitude R = 4 in terms of the standard intensity I_0. Express the intensity I of an earthquake of magnitude R = 6 in terms of the standard intensity I_0. How many times greater is the intensity of an earthquake of magnitude 6 than one of magnitude 4? In modem times the greatest loss of life attributable to an earthquake occurred in eastern China in 1976. Known as the Tangshan earthquake, it registered 8.2 on the Richter scale. How does the intensity of this earthquake Compare with the intensity of an earthquake of magnitude R = 4? Round your answer to the nearest integer. I = 1000000I_0; I = 10000I_0; 2; 15834 I =10000I_0; I = 1000000I_0; 100; 15859

Solution

R = log (I/Io)
a)
For R=4
4 = log (I/Io)
I/Io = 10^4
I = 10000*Io
Answer: 10000*Io

b)
For R=6
6 = log (I/Io)
I/Io = 10^6
T = 1000000*Io
Answer: 1000000*Io

c)
Larger by 1000000*Io/10000*Io = 100 times
Answer: 100 times

d)
For R=8.2
8.2 = log (I/Io)
I/Io = 10^8.2
I = 158489319*Io