Let's compare the energies involved in earthquakes, bomb explosions, and asteroid collisions.

**Bomb Explosion**

If a bomb containing 110 kg of plutonium (1.43 x10^{26} atoms)
is detonated, and this material undergoes fission, each atomic fission
reaction releases 2.88 x 10^{-11} Joules of energy. The total
amount of energy released in this explosion is:

EIf one megaton (= one million tons =10_{bomb}= (1.43 x10^{26}atoms) x (2.88 x 10^{-11}J/atom)E_{bomb }= 4.12 x 10^{15}J

E_{bomb}= 4.12 x 10^{15}J / (4.16 x 10^{15}J/megaton) = 0.99 megaton

Assume a 1 km radius, spherical asteroid hits the earth. What is the volume of the asteroid?

V = 4/3 pi R^{3}= 4/3 pi (10^{3}m)^{3}= 4.19 x 10^{9}m^{3}

If the asteroid is made of normal rock, with an average density
of 3500 kg per cubic meter, what is the mass of the asteroid?

M = density x volume = 3500 kg/mThe comet that hit Jupiter in July, 1994 impacted at a velocity of 60 km/sec! If the asteroid hits Earth at a velocity of 30 km/sec, what is the kinetic energy of the collision? [Note that KE = 0.5 M v^{3}x 4.19 x 10^{9}m^{3}= 1.47 x 10^{13}kg

EIf we convert this to megatons, this is equivalent to 1.6 Million megatons._{impact}= 0.5 x (1.47 x 10^{13}kg) x (30 x 10^{3}m/s)^{2}E_{impact}= 6.6 x 10^{21}J

**An earthquake**

The energy in an earthquake is usually calibrated on what we know of as the Richter scale. This is written algebraically as

log E = -2.22 + 2.57m,where E is the energy (J) and m is the magnitude of the earthquake. We can rewrite this as

E = 10For example, a magnitude 1 earthquake would release^{-2.22+2.57m}.

E_{quake=1}= 10^{0.35}= 2.2 J.

How much energy is released by a magnitude 8 (m = 8) earthquake?

EHow much energy is released by a magnitude 3 earthquake (m=3)?_{quake=8}= 10^{-2.22+2.57x8}= 10^{18.34}E_{quake=8}= 2 x 10^{18}J

EIf there are 50,000 third magnitude earthquakes every year, and only one magnitude 8 earthquake every year, how does Earth release most of its seismic energy, in big or small quakes?_{quake=3}= 10^{-2.22+2.57x3}= 10^{5.49}= 3.1 x 10^{5 }J

In 50,000 magnitude 3 quakes, the energy released would be 5 x 10^{4}x 3.1 x 10^{5 }J = 1.5 x 10^{10 }J, so a single large quake releases much more energy than an enormous number of smaller ones.

The 1945 Atomic Bomb explosion at Hiroshima released 7.9 x 10^{13}
= 10^{13.9} , or just less than 10^{14} J. We can
translate this energy release into an equivalently energetic earthquake:

We can simply solve the magnitude equation for m:

13.9 = -2.22 + 2.57 x m

m = (13.9+2.22)/2.57 = 6.27

so the Hiroshima explosion released as much energy as a magnitude 6.27 earthquake (of course, it also released much of this energy as heat, causing lots of damage from fires and also released lots of radioactive particles; so the damage from this bomb wasn't strictly related to the amount of energy released in the explosion).

The asteroid impact is 3,300 times more energetic than the magnitude 8 earthquake (it is equivalent to a magnitude 9.35 earthquake), while the bomb explosion produces only a miniscule amount of energy compared to either the earthquake or asteroid impact.E_{impact}= 6.6 x 10^{21}JE_{quake=8}= 2 x 10^{18}JE_{Hiroshima }= 7.9 x 10^{13}J