Written a few years ago, the internet guide How to destroy the Earth catalogues a series of increasingly improbable methods for terminating the existence of our planet. Southern Exposure has recently reignited interest in the subject. The guide has its moments, but as a geochemist I find it to be sadly lacking in the area of geology-based Earth destruction procedures. So without further ado, here is the isotope geochemist’s preferred way of obliterating this pale blue dot upon which we live:
Fuse the mantle.
One of the most fundamental concepts in high resolution mass spectrometry is binding energy. Simply put, some of the mass of the individual nucleons in a nucleus is converted into energy, so that the total mass of the nucleus is less than that of its components. The greater the binding energy, the larger the mass deficit, so tightly bound nuclei have measurably less mass than loosely bound ones. This difference in mass can be detected with a high resolution mass spectrometer, and is used to distinguish between ions with similar mass, such as 176Hf16O2 and 208Pb.
As explained previously, Hf and O are both more tightly bound than Pb, so the HfO2 molecule is 45 millimass units lighter than Pb, allowing us to separate them.
Binding energy is greatest at around 58 amu, so fusing lighter elements into elements in that mass range releases energy. This is the source of energy that powers the stars, and it is what I wish to use to destroy our planet.
To a first approximation, the Earth’s mantle is made of Mg and Si oxide. MgO and SiO2 comprise 87% of the mass of the mantle, with the remainder being mostly oxides of Fe, Ca, Al, and Na.
Mg, Si, and O are all substantially lighter than Fe, so considerable energy should be produced by fusing them into iron or nickel. If this energy is greater than the gravitational binding energy of the Earth, then fusing the mantle could potentially destroy the planet.
For simplicity, we will consider only two basic fusion reactions, ignoring minor isotopes and trace elements.
1. 28Si + 2 16O -> 60Ni
2. 3 24Mg+ 3 16O -> 2 60Ni
Equation 1 results in a mass loss of 35.9mAMU/60Ni, while equation 2 results in a loss of 39.1 mAMU/60Ni. Multiplying by the respective mass of SiO2 and MgO in the mantle, we react a total mass of 3.4 x1024 kg, making the total mass converted to energy 2.13 x1021kg- a mass similar to the Saturnian moon Rhea. Converting this mass to energy via E=mc2, we get a respectable energy release of 1.9x1038 joules. Note that slightly better yields can be achieved by ending the fusion reactions at 56Fe or 58Fe, instead of 60Ni. As shown below, this is quite irrelevant.
According to the International Earth Destruction Advisory Board, the gravitational binding energy of the Earth is only 2.24 x1032 Joules. So fusing the mantle into nickel provides approximately one million times more energy than is required to blow it up.
Of course, there are a few problems with this scheme. Firstly, it will probably be necessary to compress the mantle in order to trigger fusion, and the more the Earth is compressed, the greater the binding energy. However, our rather large energy excess means that we can compress the Earth to a radius of 7 meters (3/5 GM2/r, assuming a homogenous Earth) before the binding energy becomes too great to exceed with fusion. This density would be greater than that of a white dwarf or neutron star, so chances are pretty good that fusion would be initiated before that density was reached.
The second problem is that, unless the energy is somehow transferred into the core, the mantle could just blow itself into space, leaving the mars-diameter iron core behind. This core would still meet the IAU definition of a planet, so we would have failed to destroy the Earth according to the IEDAB guidelines. While the core is mostly iron and nickel already, there should be enough light elements to do the job. After all, with a million times more energy than we need, a 1% light element composition should still give us several orders of magnitude more energy than is required.
So, if you want to blow this here planet out of existence, don’t worry about antimatter guns or black holes. Just compress the planet until the mantle fuses, and that should do the job. How does one squeeze the mantle that hard? I recommend burying it under 7 x1025 sperm whales. Alternative methods are left as an exercise for the reader.