Question

Q13. Two earthquakes a and b happen to be of magnitude 5 and 6 respectively on richter scale. The ratio of the energies released eb/ea will be approximately: (a) ~64 (b) ~8 (c) ~16 (d) ~32 answer: d

Answer 1

Answer: option d) 32

The magnitude and energy of Earthquake are related by the following relation:

$M=\frac{2}{3}log_{10}\frac{E}{E_o}$

Where, M is the magnitude of the Earthquake on the Richter scale, E is the energy released by the Earthquake in Joules and $E_o$ is the energy released by the reference Earthquake.

$E_o = 10^{4.4}J$

It is given that,

$M_a=5$

$\Rightarrow 5 = \frac{2}{3} log_{10}\frac{E_a}{10^{4.4}}\\ \Rightarrow 7.5 = log_{10}E_a-log_{10} 10^{4.4}\\ \log_{10}E_a= 7.5+4.4 =11.9 \\ \Rightarrow E_a = 10^{11.9} J$

$M_b=6$

$\Rightarrow 6 = \frac{2}{3} log_{10}\frac{E_b}{10^{4.4}}\\ \Rightarrow 9 = log_{10}E_b-log_{10} 10^{4.4}\\ \log_{10}E_b= 9+4.4 =13.4 \\ \Rightarrow E_a = 10^{13.4} J$

The ratio of energies released:

$\frac{E_b}{E_a} = \frac{10^{13.4}}{10^{11.9}}=10^{1.5}=31.6$

Hence, the ratio of the energies released will be approximately: 32