Question

How much energy, in joules, is released by an earthquake of magnitude $8$?

Answer 1

Hint:The given question is totally based on the formula for energy and magnitude of earthquake. So, in order to find the solution for the given question we need to use the formula given by Gutenberg. The formula is generally known as the Gutenberg-Richter magnitude energy relation. Then we need to solve the obtained equation in order to finally conclude with the correct solution for the given question.

Complete step by step answer:
Step one
We know this fact that earthquakes release energy which can be observed in different forms such as heat energy, potential energy, or the energy stored in the form of seismic waves.
The magnitude of the earthquake in the question is given as,$R = 8$
Step two
From Gutenberg Richter magnitude energy relation, we have,
${\log _{10}}E = 1.5R + 4.8$
This can be written as,
$E = {10^{1.5R + 4.8}}$……………. (i)
Step three
Now, we need to put the values in equation (i).
After putting the values in equation (i), we get,
$E = {10^{1.5 \times 8 + 4.8}}$
$ \Rightarrow E = {10^{16.8}}$
$\therefore E = 6.3 \times {10^{16}}J$
We can observe that the amount of energy released by the magnitude of $8$ on the Richter scale is very high.
Hence, in an earthquake of magnitude $8$, the amount of energy that is released is $6.3 \times {10^{16}}J$.

Note:
The magnitude of the earthquake is measured by a device known as Richter scale. This device was made by a scientist named Charles F. Richter in the year $1935$. Generally the earthquakes occur along the edges of the continental plates and oceans. We also know this fact that the earth’s crust is made up of different pieces which are known as plates.