# Back-of-the-Envelope Calculations: Energy Released in an Earthquake

#### Summary

*Question*

A magnitude 8.5 earthquake (such as the 1964 Good Friday earthquake in Alaska) releases about 1x10^{18} joules of energy. The atomic bomb exploded over Hiroshima released about 1.5x10^{13} joules of energy. How many Hiroshima bombs would one have to explode simultaneously to equal the amount of energy released in a single magnitude 8.5 earthquake?

## Assessment

*Answer*

67,000 (!).If you want to divide 1x10^{18} by 1.5x10^{13}, just subtract the exponents (18-13) to get 10^{5}, and divide 1 by 1.5 to get .67, giving you .67x10^{5}, or 6.7x10^{4} (67,000).

## References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope (more info) : This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.

## Controlled Vocabulary Terms

**Subject**: Geoscience:Geology:Structural Geology:Stress/Strain/Strain Analysis, Environmental Science:Natural Hazards:Earthquakes

**Resource Type**: Activities:Classroom Activity:Short Activity

**Special Interest**: Quantitative, Hazards

**Grade Level**: High School (9-12), College Lower (13-14), College Upper (15-16)

**Quantitative Skills**: Estimation

**Ready for Use**: Ready to Use

**Theme**: Teach the Earth:Course Topics:Environmental Science, Teach the Earth:Teaching Topics:Earthquakes, Teach the Earth:Course Topics:Structural Geology, Teach the Earth:Incorporating Societal Issues:Hazards

**Topics**: Solid Earth, Chemistry/Physics/Mathematics