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:
~ 32
The Richter scale is logarithmic, so a difference of one unit in magnitude does not mean an earthquake is merely slightly stronger - it corresponds to a large multiplication of the energy released.
The relationship between energy and magnitude is given by log E = a + 1.5 M, which means that the energy ratio for two earthquakes differing in magnitude by ∆M is 10 raised to the power 1.5 × ∆M.
Here the magnitudes are 5 and 6, so ∆M = 6 − 5 = 1. The energy ratio is therefore 10 raised to the power 1.5 × 1, that is 10 to the power 1.5.
Now 10 to the power 1.5 is the same as 10 × the square root of 10, which is 10 × 3.162 = 31.62, or approximately 32.
So earthquake B releases about 32 times as much energy as earthquake A, even though its magnitude number is only one higher. It is worth separating two facts often confused: each unit of magnitude corresponds to a tenfold increase in the amplitude of ground motion, but about a thirty-twofold increase in energy released. The option of 10 is not offered here precisely because the question asks about energy rather than amplitude.
Hence the ratio of energies Eₑ/Eₐ is approximately 32.
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