A magnitude 6.5 earthquake occurs. Estimate the total energy released using the empirical relation $E = 1 0^{1.5 M + 4.8}$ joules. Round to two significant figures.

medium 2 marks Class 8 · Science · Some Natural Phenomena

Answer

3.6 \times 1 0^{14} J

The correct answer is $3.6 \times 1 0^{14} J$ — Round $3.55 \times 1 0^{14}$ to two significant figures giving $3.6 \times 1 0^{14}$ J.

Step-by-step solution

Write the given formula $E = 1 0^{1.5 M + 4.8}$ .
Substitute $M = 6.5$ into the formula.
Calculate $1.5 M = 9.75$ .
Add $4.8$ to get $14.55$ as the exponent.
Compute $1 0^{14.55}$ using $1 0^{0.55} \approx 3.55$ to get $3.55 \times 1 0^{14}$ .
Round $3.55 \times 1 0^{14}$ to two significant figures giving $3.6 \times 1 0^{14}$ J.

Common mistake: Forgetting to add 4.8 to 1.5M before exponentiation

Concept tested: Earthquake energy calculation