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…

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asked Apr 6, 2020 164k views

1 Answer

Sscswapnil · Answer 1 · 2020-04-09T20:14:58+0000

Answer:

Japan :
E=2.8183829313* 10^(18)

California :
E=2.8183829313* 10^(15)

Explanation:

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

$M=(2)/(3)\log (E)-3.2$

where E is the energy of the quake in joules.

Add 3.2 on both sides.

$M+3.2=(2)/(3)\log (E)$

Multiply both sides by 3/2.

$(3)/(2)(M+3.2)=(3)/(2)* (2)/(3)\log (E)$

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

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* 10^(18)

Therefore, the energy released by earthquake in japan is
.

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* 10^(15)

Therefore, the energy released by earthquake in California is
.