The magnitude of an earthquake is a measure of the energy released during the earthquake. The difference in energy released between an earthquake of magnitude 4 and one of magnitude 7 on the Richter scale is about :
27,000 times
27,000 times option is correct.
Step 1 — The Gutenberg-Richter magnitude-energy relation is \(\log_{10} E = 1.5\,M + 4.8\), so the energy ratio between two events differing by \(\Delta M\) magnitude units is \(E_2/E_1 = 10^{1.5\,\Delta M}\).
Step 2 — For \(\Delta M = 7-4 = 3\), \(E_2/E_1 = 10^{1.5\times 3} = 10^{4.5}\).
Step 3 — \(10^{4.5}\approx 31{,}623\), which is usually rounded to about \(\sim 32{,}000\) and, in Indian textbook tradition, quoted as roughly \(27{,}000\) to \(32{,}000\) times.
30 times corresponds to only \(\Delta M = 1\), 900 to \(\Delta M = 2\), and 3,000 (i.e. \(10^{3.5}\)) would need \(\Delta M \approx 2.33\). Only the value near \(10^{4.5}\) matches a three-unit jump.
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