Question

Thor, the god of war, creates a thunderous sound as he rides over the clouds in his chariot. It is a sound equivalent to an earthquake of magnitude 4.6.How much energy does Thor create?Give your answer in scientific notation with at least 3 decimal positions.

Answer 1

The magnitude of the earthquake is related to the released energy E via the equation

$\log _{10}E=4.4+1.5M$

where M is the magnitude of the earthquake. Given that M is equal to 4.6, the equation can be simplified as:

$\begin{gathered} \log _{10}E=4.4+1.5(4.6) \\ \log _{10}E=4.4+6.9 \\ \log _{10}E=11.3 \end{gathered}$

We both raise the two sides of the equation by 10 to eliminate the log on the left-hand side and solve, as follows:

$\begin{gathered} E=10^{11.3} \\ E=1.99526231\times10^{11} \end{gathered}$

Since the question wants us to write the answer in at least 3 decimal points, the final answer would be

$E=1.995\times10^{11}J$

Answer: The energy Thor created is about 1.995 x 10^11 Joules.