Question

The Richter scale measures the intensity of earthquakes on a logarithmic scale. The magnitude of an earthquake on the Richter scale can be defined by M=2/3log(E)-3.2, where E is the energy of the quake in joules. The 2011 Tohoku earthquake in Japan measured 9.1 on the Richter scale. The 1999 Hector Mine earthquake in eastern California had a magnitude of 7.1. Calculate the energy released by each earthquake.

Answer 1

Answer:

Japan : $E=2.8183829313\times 10^{18}$

California : $E=2.8183829313\times 10^{15}$

Step-by-step explanation:

The magnitude of an earthquake on the Richter scale can be defined by

$M=\frac{2}{3}\log (E)-3.2$

where E is the energy of the quake in joules.

Add 3.2 on both sides.

$M+3.2=\frac{2}{3}\log (E)$

Multiply both sides by 3/2.

$\frac{3}{2}(M+3.2)=\frac{3}{2}\times \frac{2}{3}\log (E)$

$1.5M+4.8=\log (E)$

$10^{1.5M+4.8}=E$               $[\because \log x=a\Rightarrow x=10^a]$

$E=10^{1.5M+4.8}$           .... (1)

It is given that the 2011 Tohoku earthquake in Japan measured 9.1 on the Richter scale.

Substitute M=9.1 in equation (1).

$E=10^{1.5(9.1)+4.8}$

$E=10^{18.45}$

$E=2.8183829313\times 10^{18}$

Therefore, the energy released by earthquake in japan is $E=2.8183829313\times 10^{18}$.

It is given that the 1999 Hector Mine earthquake in eastern California had a magnitude of 7.1.

Substitute M=7.1 in equation (1).

$E=10^{1.5(7.1)+4.8}$

$E=10^{15.45}$

$E=2.8183829313\times 10^{15}$

Therefore, the energy released by earthquake in California is $E=2.8183829313\times 10^{15}$.