The Fission Myth

Written: 1998.11.08
Last Revised: 1999.04.25

Some trekkies have advanced the theory that the Death Star caused all of the fissionable elements in Alderaan to undergo fission at once. This is basically a permutation of the idea that all of the energy came from the target rather than the source. However, there are only a few possible modes of nuclear fission. Of these, the most common (and applicable) is neutron capture followed by spontaneous fission. This is the mechanism used in atomic bombs and 20th century nuclear fission reactors. Photo-disintegration (absorption of a highly energetic gamma ray, which excites the nucleus to a state where the nuclear binding force is overcome) or extreme high-energy collision (such as the particle collisions in a large particle accelerator) can cause nuclei to fission, but they cannot produce net-positive power- photo-disintegration consumes power because it is only effective on small nuclei so it results in an increase in energy states, and extreme high-energy collision requires so much energy on the part of the impactor that the energy yield doesn't make up for the cost. Therefore, we will discuss nuclear fission through neutron capture.

The basic theory is simple: bombard low-stability heavy metals such as uranium with neutron radiation, and some of the neutrons will be captured. Once they have been captured, the result is a compound nucleus in an excited state. This state of excitation, combined with the Coulomb repulsion between the protons in the nucleus, is enough to overcome the strong nuclear forces holding the nucleus together. As a result, the nucleus splits apart into two smaller nuclei.

Why do heavy metals easily undergo fission? It happens because of the curve of binding energy per nucleon. Although binding energy climbs steadily with increasing atomic number, binding energy per nucleon only climbs until it reaches a peak between nuclei containing between 50 and 80 nucleons. After this peak, it begins to drop off again. As a result, the ratio between Coulomb repulsion and nuclear binding force can approach unity with certain heavy metal isotopes. If those isotopes are made to oscillate violently (by the addition of a neutron, for example), then the oscillation may distort the shape of the nucleus enough that Coulomb repulsion can literally tear the atom apart from within, in spite of the nuclear binding force.

U-235 is highly susceptible to nuclear fission because low-energy neutrons (so-called "thermal neutrons") can cause fission due to its high ratio of protons to neutrons. However, it is an extremely rare isotope of uranium, comprising less than 1% of the total supply on Earth. U-238 is by far the most common isotope of uranium, but it is not easily fissioned. High-energy neutron radiation (~1.3 MeV or higher) is required to induce fission in U-238, which is why refined uranium (with increased levels of U-235, up to 4.5% for power plants and 90% for weapons) has always been used in weapons and most types of nuclear power plants. The Canadian CANDU nuclear reactor system is currently the only major nuclear reactor design in the world which can run on unrefined uranium, thanks to the superior effectiveness of its heavy-water moderator.

However, this is all essentially background trivia. In order to induce complete fission in the uranium atoms scattered through the mass of a planet, the Death Star would have to subject the entire planet to an intense neutron radiation flux, which is impractical for numerous reasons:

Is it possible to induce fission in the fissionable materials scattered throughout a planet's mass? Yes, given some extreme hypothetical situations. But would the fission produce more energy than the neutron beam required to induce fission? No. The neutron beam (in addition to having a completely different appearance than the superlaser in ANH) would need to carry so much energy that fission would be utterly redundant and insignificant. Therefore, nuclear fission utterly fails as an explanation for the Death Star's destruction of Alderaan.

As a final note, it is worth mentioning that a planetary core is not composed mostly of heavy metals, contrary to some popular beliefs. It is composed mostly of iron. The Earth's chemical composition, by mass, in decreasing order, is:

Iron

34.6%

Oxygen

29.5%

Silicon

15.2%

Magnesium

12.7%

Nickel

2.4%

Sulfur

1.9%

Titanium

0.05%

Note that every one of those elements is a fairly stable, light element, with atomic numbers between 8 and 28. This is hardly surprising. Although the universe does contain heavy fissionable elements, those elements are present in extremely small quantities.

The Fusion Myth

Naturally, since fission is infeasible on a planetary scale because of the inherent difficulties and the rarity of easily fissioned materials in a planet's mass, some trekkies turn to fusion as an alternate explanation (anything would apparently be better than simply admitting that it is impossible to blow a planet apart without using a staggering amount of energy). Nuclear fusion produces more energy per unit mass than nuclear fission. While the theoretical energy density for perfect fission is roughly 8.5E13 J/kg, the theoreteical energy density for perfect fusion is roughly 6.3E14 J/kg, an increase of more than 7 times.

However, nuclear fusion is even more difficult to induce than nuclear fission. It occurs naturally in stars, but a star must compress and heat hydrogen plasma to temperatures in excess of 15 million K and pressures in excess of 250 billion bars (25 billion MPa). At these temperatures and pressures, the hydrogen plasma is compressed to roughly 1.5E5 kg/m³, which is 13 times the density of lead. Note that it is still gaseous at this density! The temperature and pressure increase the frequency and velocity of proton-proton collisions to the point that some of those collisions will occur at sufficient speed to overcome Coulomb repulsion and cause nuclear fusion. The hydrogen-hydrogen fusion reaction is but the first stage of a three-stage fusion reaction. In the first stage, four hydrogen ions fuse to form two deuterons, two positrons, and two neutrinos. In the second stage, the deuterons from the first stage fuse with two more hydrogen ions to form two helium atoms (He3) and two gamma rays. In the third stage, the two He3 ions from the second stage fuse to form a heavier helium isotope (He4), plus two hydrogen ions. The net result is that four hydrogen ions turn into an alpha particle (He4) and two positrons, with a total energy release of approximately 26.2 MeV.

However, the reaction rate of nuclear fusion in the sun's core is extremely low. In spite of the enormous temperatures and pressures, the sun only produces ~1E12 kg/s of deuterium per second, because only one in 1E26 proton-proton collisions will result in fusion. In other words, the sun's reaction rate is so low that only 1/2E18 of its mass reacts each second! This is very fortunate for the people of Earth, otherwise the sun's lifespan would be greatly shortened and its intensity would be far too high for any terran life forms to survive. However, this does indicate the difficulty of inducing fusion in hydrogen- even at such enormous temperatures and pressures as those found in the sun's core, fusion occurs at infinitesimally slow rates. It is only the sheer size of the sun that causes its large overall power output.

So, how difficult would it be to induce fusion in the hydrogen scattered throughout an Earth-like planet's mass? First, the amount of hydrogen in the Earth's crust is insignificant relative to its mass- less than 4E19 kg out of the total 6E24 kg. Furthermore, all of the Earth's hydrogen is in its crust- the mantle and core are composed of heavier elements like iron. Therefore, we can easily determine the difficulty of producing the necessary conditions to duplicate the hydrogen particle density and temperature in the core of the sun, to induce fusion. Obviously, we know that we need to heat the entire planet to more than 15 million K if we are to achieve fusion-generating temperatures. But we also know that we need an average hydrogen atom density of roughly 1.5E5 kg/m³ (the density of other materials is meaningless, because fusion rates are based on reactant density), so all of an Earthlike planet's 4E19 kg of hydrogen would have to be compressed into a sphere of less than eighty kilometres diameter! Furthermore, since there is no conceivable way for the Death Star beam to gather all of a planet's hydrogen, compress it, and then teleport it to the centre of the planet to create the necessary expansion dynamics, the Death Star could only accomplish this feat in one of two ways:

The conclusion to this section is similar to the conclusion for the fission section. Is it possible to induce fusion in the hydrogen molecules scattered through the crust of a planet? Yes. But would this fusion produce more energy than the energy required to induce fusion in the first place? Absolutely not.



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