Finally, let’s look at the energies involved in fission and fusion. When a heavy nucleus undergoes fission, the average binding energy per nucleon goes from 7 MeV (in round numbers) in the “parent” nucleus to about 8 MeV in the “daughter” nuclei, which are closer to the “most stable” iron. The 1 MeV per nucleon of energy that is released multiplied by, say, 236 nucleons in the fissioning nucleus gives a total calculated energy release of 236 MeV (very close to the measured value). Heading to the other end of the periodic table, we find that the fusing of two deuterons to make an alpha particle releases some 6 MeV per nucleon (the 7 MeV per nucleon in the alpha particle minus the 1 MeV per nucleon in the deuterons). For other fusion reactions in light nuclei, such as between protons in the Sun or between deuterons and tritons in an H bomb, the energy release per nucleon is similar. In summary: Although the total energy released per event is greater for fission than for fusion, the energy released per unit mass is some six times greater for fusion than for fission. This comparison doesn’t carry over directly to bombs, since the mass of a bomb includes the mass of ancillary structures, not just the mass of the fuel, but it remains true that an H bomb is more “efficient” than an A bomb. For a given mass, it releases more energy. And both release at least 100,000 times more energy per unit mass than dynamite or TNT.
Radiation as Stuff
Let me explain what was special about the radiation-implosion idea (the 1951 insight of Edward Teller and Stan Ulam that replaced the unattainable runaway Super with the successful equilibrium Super). It has to do with the temperature of matter and radiation and the division of energy between matter and radiation.
That matter has a certain temperature is a familiar idea. The air and the walls in your living room may be at 68 degrees Fahrenheit, or 20 degrees Celsius. The inside of your refrigerator may be at 5 degrees Celsius, your body at 37 degrees Celsius. The temperature of the Sun’s surface is 5,500 degrees Celsius. All of these numbers can be rendered, too, in a unit that physicists tend to favor, the kelvin. A temperature in kelvins is the number of Celsius degrees above absolute zero: 293 K for the living room, 278 K for the refrigerator, 310 K for body temperature, and about 5,770 K for the Sun’s surface. The center of the Sun is at about 15 million K, and the temperature generated in the core of a fission bomb—which is also roughly the temperature needed to sustain thermonuclear burning—is even greater, some 50 million K.
That radiation may have a temperature is a less familiar idea. The radiation emanating from the Sun’s surface mimics the temperature at the surface, or 5,770 K. If it were coming at you from all sides—if you were literally bathed in it—it would vaporize you like a comic-book ray gun. Fortunately, it impinges on you from only a tiny range of angles, so the worst it can do is give you a sunburn.[38] Filling up all of “empty” space in the universe is radiation, the so-called cosmic background radiation, in which we are indeed bathed. It has a temperature of 2.7 K—very cold indeed but easily measured. These are examples of electromagnetic radiation, which, from a modern perspective, consists of photons running hither and thither. Within your living room, there is actually radiation with the same temperature as that of the walls and the air molecules—tenuous but definitely there.
Not all radiation has to have a temperature. Your mobile phone, for example, is emitting and absorbing radiation, but that radiation has no defined temperature because it is not in equilibrium with matter. When matter and radiation are constantly exchanging energy, they can come to a common temperature, just as the walls and the photons bouncing around in your living room do.[39] As you can surmise, all of this has something to do with thermonuclear weapons. The intention of the classical Super design was for the temperature of the exploding thermonuclear fuel to outstrip the temperature of radiation emitted by the “burning” fuel, so that as much as possible of the energy being generated remained in the matter and as little as possible of it got “lost” in radiation. In the Teller-Ulam design, by contrast, matter and radiation remain in equilibrium and maintain pretty much the same temperature. I discussed at the end of Chapter 1 why this idea didn’t surface until 1951, nearly a decade after physicists first started discussing how to make an H bomb.
Now to energy. When something gets hotter, it also gains more energy, but not always in direct proportion—in fact, for radiation, very far from a direct proportion.
Let’s suppose that you are a hobbyist who keeps a cubic meter of deuterium (heavy hydrogen) in a large box in your back yard. Your container is a cube one meter—about three feet—on a side. You are interested in the temperature and the energy of the deuterium and of the radiation that is trapped along with the deuterium gas inside the box. Since you are an amateur physicist as well, you calculate that on a warm summer day, with the temperature around 80 degrees Fahrenheit, or 300 K, and with a pressure in your box of one atmosphere, the total energy in the random motion of all the deuterium molecules in the box is 150,000 joules. (This is the energy of what is called the “translational” motion of the molecules as they bounce around from place to place. It is the energy associated with temperature, and doesn’t include the vibrational and rotational energy of the molecules.) What, you then ask yourself, is the energy of the trapped radiation in the box? You can calculate this, too, and you find it to be six millionths of one joule—25 billion times less than the energy in the matter. You can also calculate the pressure exerted by that radiation on the walls of its container, and find it to be twenty trillionths of one atmosphere. So the radiation in the box (and in your living room) is tenuous indeed.
You could build a fire under your box of deuterium and explore how much the energy of matter and radiation change. The answer would be not much for the range of temperatures you could actually achieve. So, instead, you decide to do a thought experiment—what Einstein and his German-speaking colleagues used to call a Gedankenexperiment. What, you ask yourself, would happen to the energy in the matter and the radiation if you raised the temperature of the box from 300 K to 30 million K—not enough to trigger a thermonuclear explosion, but getting close. That would be a factor of temperature increase of 100,000. The energy in the matter, it turns out, would increase by a factor of 400,000 rather than 100,000. This is because at that temperature, where there used to be one deuterium molecule there would now be two deuterium nuclei and two electrons—four particles where there used to be one. The energy in the matter is then some 60 billion joules, or the equivalent of 15 tons of high explosive (0.015 kilotons).
You might then think, “Well, the energy in my hypothetical super-hot box isn’t enough to destroy a city, but it could do in a village.” But wait. What has happened to the energy in the radiation in this thought experiment? Maybe that changes the picture. It does indeed. The energy in a given volume of radiation goes as the fourth power of the temperature. If you double the temperature (the absolute temperature, in kelvins), the energy in the radiation increases by a factor of sixteen (2 to the 4th power). If you increase the radiation temperature by a factor of ten, the radiant energy increases by a factor of ten thousand (10 to the 4th power). If you increase the temperature by a factor of 100,000, as you have done in your thought experiment, the energy in the radiation increases by the quite enormous factor of 1020, or 100 billion billion. The once-tenuous radiation, which originally accounted for one twenty-five billionth of the energy in your box, now accounts for 99.999 percent of it. The energy in the one cubic meter of radiation at a temperature of 30 million K is, in the units favored by weaponeers, 15 kilotons. And its pressure is correspondingly elevated, to 2 billion atmospheres.
38
Of course, there is a lot of “best” that sunlight can do, too—warming Earth, energizing plants, and, with the help of solar cells, generating electricity.
39
Compact fluorescent bulbs and light-emitting diodes (LEDs) are often marked with an “effective temperature.” If you buy a bulb that is marked “2,700 K,” it does not, of course, mean that the bulb reaches such a high temperature. Far from it. It means that the color spectrum emitted by the bulb is similar to that of light from a source at 2,700 K, strong in the red, weak in the blue. If the bulb is marked “5,000 K,” its colors are similar to those of a hotter source, strong in the blue, weak in the red. Interestingly, we call the reddish tone of the 2,700-K bulb “warm” and the bluish tone of the 5,000-K bulb “cool.”