Let's compare the energies involved in earthquakes, bomb explosions, and asteroid collisions.
If a bomb containing 110 kg of plutonium (1.43 x1026 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:
Ebomb = (1.43 x1026 atoms) x (2.88 x 10-11 J/atom)If one megaton (= one million tons =106 tons) of TNT releases 4.16 x 1015 J, what size warhead (in megatons) would this 110 kg plutonium bomb correspond to?
Ebomb = 4.12 x 1015 J
Ebomb = 4.12 x 1015 J / (4.16 x 1015 J/megaton) = 0.99 megatonAsteroid Impact
Assume a 1 km radius, spherical asteroid hits the earth. What is the volume of the asteroid?
V = 4/3 pi R3 = 4/3 pi (103 m)3 = 4.19 x 109 m3
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/m3 x 4.19 x 109 m3= 1.47 x 1013 kgThe 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 v2, where M is the mass and v is the velocity of the impacting body.] [gm cm/s will give ergs; kg m/s will give Joules]
Eimpact = 0.5 x (1.47 x 1013 kg) x (30 x 103 m/s)2If we convert this to megatons, this is equivalent to 1.6 Million megatons.
Eimpact = 6.6 x 1021 J
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 = 10-2.22+2.57m.For example, a magnitude 1 earthquake would release
Equake=1 = 100.35 = 2.2 J.
How much energy is released by a magnitude 8 (m = 8) earthquake?
Equake=8 = 10-2.22+2.57x8 = 1018.34How much energy is released by a magnitude 3 earthquake (m=3)?
Equake=8 = 2 x 1018 J
Equake=3 = 10-2.22+2.57x3 = 105.49 = 3.1 x 105 JIf 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?
In 50,000 magnitude 3 quakes, the energy released would be 5 x 104 x 3.1 x 105 J = 1.5 x 1010 J, so a single large quake releases much more energy than an enormous number of smaller ones.A comparison: Bombs, Earthquakes and Impacts
The 1945 Atomic Bomb explosion at Hiroshima released 7.9 x 1013 = 1013.9 , or just less than 1014 J. We can translate this energy release into an equivalently energetic earthquake:
We can simply solve the magnitude equation for m:Compare these three events
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).
Eimpact = 6.6 x 1021 JThe 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.
Equake=8 = 2 x 1018 J
EHiroshima = 7.9 x 1013 J