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decimal places, so they don’t usually use kilograms to measure mass. Instead they use a unit called the electron volt, which is actually a measurement of energy. An electron volt is the amount of energy an electron gets when it is accelerated through a potential difference of 1 volt. This is a mouthful, and we are again in danger of covering ourselves in chalk dust. In more normal-sounding language, if you get a 9 volt battery and build a little particle accelerator out of it, you would be able to give an electron 9 electron volts of energy. The electron volt is turned into a mass by dividing it by c2 (remember E = mc2). In this rather more convenient language, the hydrogen atom has a smallest mass, which is 13.6 eV/c2 less than the masses of the proton (938,272,013 eV/c2) and electron (510,998 eV/c2) combined (1 eV is the abbreviation for an energy of 1 electron volt). Notice that by keeping a factor of c2 “in the units,” it is easy to figure out how much energy is stored within a proton at rest. Since the energy is obtained by multiplying the mass by c2, the c2 factors cancel out and the energy is just 938,272,013 eV.

Notice also that the mass of a hydrogen atom is smaller, not bigger, than the sum of its component parts. It is as if the atom has some negative energy stored within it. There is nothing mystical about negative energy in this context: “Negative stored energy” just means that it takes effort to dismantle the atom, and it often goes by the name “binding energy.” The next smallest mass of a hydrogen atom is 10.2 eV/c2 smaller than the sum of its parts.7 The mystical-sounding and oft-misunderstood quantum theory actually derives its name from the fact that masses like these come in discrete (“quantized”) values. For example, there is no hydrogen atom with a mass 2 eV/c2 bigger than the smallest mass. This is really all there is to the word “quantum.” The different masses actually correspond to the electrons being in different orbits around the atomic nucleus, which in the case of hydrogen is a single proton.

That said, one has to be very careful in picturing electron orbits, because they are not really like the orbits of planets around the sun. Loosely speaking, the atom with the smallest mass has the electron closer to the proton than the atom with the next smallest mass, and so on. The hydrogen atom with the electron as close as it can be to the proton is said to be in its “ground state” and it is as light as it can be. Add just the right amount of energy and the electron will jump up to the next available orbit and the atom will become a bit heavier, simply because a bit of energy has been added. In that sense, adding energy to an atom is like winding up the spring in a mousetrap.

All of this does beg the question of how we know such fine detail about hydrogen atoms. Surely we don’t go around measuring these tiny mass differences using weighing scales? At the heart of the quantum theory is an equation called the Schrödinger wave equation, and we can use it to predict what the masses should be. Legend has it that Schrödinger discovered the equation, one of the most important in modern physics, while on a winter sojourn with his mistress in the Alps over Christmas and New Year’s of 1925-1926. Quite how he explained this to his wife is rarely discussed in physics textbooks. We can only hope his mistress enjoyed the fruits of his labors as much as the generations of physics students who know the eponymous equation by heart. The calculation is not too difficult for an atom as simple as hydrogen, and it has graced many an undergraduate examination paper. But mathematical tractability means little without the corroborating evidence provided by experiments. Fortunately, the results of the quantum nature of atomic structure are pretty easy to observe. In fact, we all observe them every day. There is a general rule in quantum theory that roughly goes like this: Left alone, a heavier thing will turn into a lighter thing if at all possible. It is not a hard concept to understand. If the thing is left alone it