Answer: The magnitude rating for an earthquake causing an amplitude 10,000,000 times [tex]I_o[/tex] is 7.
Explanation:
Richter scale is defined as the scale which expresses the magnitude of earthquake on the basis of the seismograph oscillations.
The equation used to measure the magnitude of an earthquake on Richter scale is:
[tex]M=log_{10}\frac{I}{I_o}[/tex]
where
I = amplitude registered on seismograph 100 km away from seismic center = [tex]10,000,000I_o[/tex]
[tex]I_o[/tex] = small amplitude
Putting values in above equation, we get:
[tex]M=\log_{10}(\frac{10000000I_o}{I_o})\\\\M=7[/tex]
Hence, the magnitude rating for an earthquake causing an amplitude 10,000,000 times [tex]I_o[/tex] is 7.
