Earthquake Intensity On the Richter scale, the magnitude R of an earthquake of intensity I is given by

R = (ln I - ln I0) / ln 1o

Where 10 is the minimum intensity used for comparison. Assume 10 = 1.

(a) Find the intensity of the March 11, 2011 earthquake in Japan for which R = 9.0.

(b) Find the intensity of the January 12. 2010 earthquake in Haiti for which R = 7.0.

(c) Fiind the factor by which the intensity is increased when the value of R is doubled.

(d) Find dR/dl.

(A) 999 734 198.4

B) 9999043.54

C) the intensity L is squared when R is doubled

D) dR/dL = 1 / (Lln10)

Step-by-step explanation:

R = (In L - ln Lo) / ln 10

Since Lo = 1 and ln 1 = 0

Therefore,

R = ln L / ln 10

(A) Since R = 9

In L = Rln10

In L = 9 ln10 = 20.723

L = exp (20.723) = 999 734 198.4

Therefore, the intensity of earthquake in Japan = 999 734 198.4

(B) when R = 7

In L = Rln10

In L = 7ln10 = 16.118

L = exp (16.118) = 9999043.54

Therefore the intensity of earthquake in Haiti = 9999043.54

(C) when R is doubled, let say R = 14

L = exp (14ln10) = 99980871640000

Then the ratio of L (R=14) and L (R=7)

L (R=14) / L (R=7) = 99980871640000/9999043.54 = 9999043.53

Since L (R=14) / L (R=7) = L (R=7)

Therefore, the intensity L is squared when R is doubled

D) R = lnL/ln10

dR/dL = 1 / (Lln10)