Question

In 1925, Santa Barbara experienced a major earthquake of magnitude 6.8. In 1978, another major earthquake hit the area with a magnitude of 5.2. How much more energy did the 1925 earthquake release than the 1978 earthquake?Give your answer in scientific notation with at least 3 decimal positions.

Answer 1

We will have the following:

First, we know that the Richter scale follows a base 10 log of energy we will have the following data from this equation:

$\log (E)=4.4+1.5M$

1925:

$\log E=4.4+1.5(6.8)\Rightarrow_{}\log _{}(E)=14.6$$\Rightarrow E^{}=10^{14.6}\Rightarrow E\approx3.981\cdot10^{14}$

So, the energy released by the earthquake with a magnitude of 6.8 in 1295 was os approximately 3.981*10^14 Joules.

1978:

$\log (E)=4.4+1.5(5.2)\Rightarrow\log (E)=12.2$$\Rightarrow E=10^{12.2}\Rightarrow E\approx1.585\cdot10^{12}$

Now, we determine the difference in energy released:

$E_f=3.981\cdot10^{14}-1.585\cdot10^{12}\Rightarrow E_f\approx3.965\cdot10^{14}$

So, the earthquake in 1925 released approximately 3.965*10^14 more joules than the earthquake in 1978.