The moment magnitude scale is used by seismologists to express the sizes of earthquakes. The scale is

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The moment magnitude scale is used by seismologists to express the sizes of earthquakes.


The scale is calculated using the formula


image


where S is the seismic moment in dyne cm.


a. Find the magnitude of an earthquake with a seismic moment of 2.24 × 1022 dyne cm.


b. Find the seismic moment of an earthquake with


i. Magnitude 6 


ii. Magnitude 7


c. Using your answers to part b or otherwise, show that an earthquake of magnitude 7 is approximately 32 times as powerful as an earthquake of magnitude 6.

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