On the Richter scale, the magnitude R of an earthquake is given by the formula:

Question

On the Richter scale, the magnitude R of an earthquake is given by the formula:
R= log(I/Io)
where I is the intensity of the earthquake being measured and Io is the standard reference intensity.
a) Express the intensity I of an earthquake of a magnitude R=5 in terms of the standard intensity Io.
b) Express the intensity I of an earthqake of magniture R=8 in terms of the standard intensity Io. How many times greater is the intensity of an earthquake of magnitue 8 than one of magnituge 5?
c) In modern times, the greatest loss of life attribuatable to an earthqake occurred in eastern China in 1976. Known as the Tangshan earthqake, it registered 8.2 on the Richter scale. How does the inensity of this earthqake compare with the intensity of an earthquake of magnitude R=5?

Explanation / Answer

a) 5=log(I/I0)

Take 10 to the power of both sides to get

105=100,000=I/I0

Multiply by I0 on both sides to get

I=100,000I0

b) 8=log(I/I0)

Take 10 to the power of both sides to get

108=100,000,000=I/I0

Multiply by I0 on both sides to get

I=100,000,000I0

To compare the intensity, take the intensity at R=8 and divide by the intensity at R=5, so

100,000,000I0/100,000I0=1,000, so 1,000 ties more intense.

c) 8.2=log(I/I0)

Take 10 to the power of both sides to get

108.2=I/I0

Multiply by I0 on both sides to get

I=108.2I0

To compare the intensity, take the intensity at R=8.2 and divide by the intensity at R=5, so

108.2I0/100,000I0=about 1584.89 times more intense.

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