Chemical Versus Nuclear Reactions Samuel Dull

March 24, 2018 Submitted as coursework for PH241, Stanford University, Winter 2018

What is a Chemical Reaction? What is a Nuclear Reaction?

Fig. 1: Average nuclear binding energy as a function of atomic number. [1] (Source: Wikimedia Commons)

An atom is the smallest unit of matter that possesses the properties of a chemical element. Atoms are made up of positively-charged protons, neutrally-charged neutrons, and negatively charged electrons. The protons and neutrons - collectively called nucleons - are held together in the nucleus by the strong nuclear force. The electrons, which have almost 2,000 times less mass than the nucleons, are held in orbit around the nucleus by the electromagnetic force. [1] The strong nuclear force and the electromagnetic force are two of the four fundamental forces currently known, the others being the weak nuclear force and gravity.

The fundamental difference between chemical reactions and nuclear reactions is which subatomic particles are rearranged in the transformation. While chemical reactions - such as the rusting of metal or the burning of wood - involve the redistribution of electrons between atoms, nuclear reactions involve the redistribution of nucleons. For example, the electrolysis of water is a chemical reaction in which the electrons orbiting the hydrogen and oxygen nuclei are rearranged such that they are no longer shared between each other but are shared with another hydrogen and oxygen nuclei, respectively. Alternatively, in the proton-proton nuclear fusion reaction, the nuclei of two hydrogen atoms merge together to form helium. It is worth noting that elements are identified by the number of protons in their nuclei, so only nuclear reactions can form different elements.

Currently, chemical reactions are carried out for a remarkable range of applications, including the production of fuels, plastics, soaps and detergents, and medicines. Yet, while chemical reactions can be considered the "jack of all trades," nuclear reactions are certainly the master of one: generating useable energy. The amount of energy generated by the fission of one kilogram of U-235 is three million times greater than that generated from the combustion of one kilogram of coal. [2]

Why Do Reactions Release Energy?

Chemical reactions are deemed exothermic if they release energy and endothermic if they absorb energy. Whether a reaction is exothermic or endothermic is determined by relative energies of the starting materials and the ending materials. For example, nitrogen gas is highly stable and synonymously low in energy. If it reacts with hydrogen gas to form ammonia, a chemical that is higher in energy, energy must be absorbed from the environment for the reaction to proceed. This reaction is therefore endothermic. For chemical reactions, determining the relative energies of the species involved is the extraordinarily complex subject of physical chemistry. However, for a first approximation, one can often predict the relative energies of compounds by the strength of the bonds they contain.

For all practical purposes, nuclear reactions are carried out exothermically. That is, high energy species are converted to low energy species, and the energy released is used to do work. Fortunately, for nuclear reactions, the relative energies of species is well-defined by the nuclear binding energies of each element, as shown in Fig. 1. The nuclear binding energy is defined as the amount of energy that would be required to disassemble the nucleus of an atom. The relative binding energy of each element is determined by a tradeoff between the strong nuclear force pulling nucleons together and the electrostatic repulsion of the protons. Because the strong nuclear force is a short range interaction, additional nucleons initially contribute stability to the atom but eventually become unfavorable due to electrostatic repulsion. As shown in Fig. 1, iron possesses the most stable nucleus. Therefore, elements lower in atomic number than iron can merge, or fuse, together to form a more stable element, thereby releasing energy. Conversely, elements greater in atomic number than iron can undergo fission to form more stable elements, again releasing energy. But why is the release of energy from a nuclear reaction so much greater than that from a chemical reaction?

Why Are Nuclear Reactions So Much More Explosive?

As shown in Fig. 1, the energy stored in a nuclear bond is on the order of 1 MeV. A typical chemical bond, on the other hand, stores energy on the order of 1eV, approximately one million times less. [1] Two main factors contribute to the energy density of a nucleus. First, despite being limited to a range of the diameter of a medium-sized nucleus, the strong nuclear force is 137 times more powerful than the electromagnetic force at a given distance. [1] Therefore, much more energy is stored between nucleons than between an electron and a proton. And second, the nucleus is far more massive than the surrounding electron cloud, as more than 99.94% of the mass of an atom resides in the nucleus. [3] Of course, mass and energy are interrelated according to Einstein's famous formula, E = mc2. It is for this reason that the so-called "mass defect" associated with nuclear reaction corresponds to a large amount of energy relative to that observed by a reaction involving strictly electrons. With those two factors in mind, it is perhaps less surprising that a kilogram of uranium could power the entire United States for three minutes.

© Sam Dull. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] E. Segre, Experimental Nuclear Physics, Vol. 2 (Wiley, 1953).

[2] J. Bernstein, Nuclear Weapons: What You Need to Know (Cambridge University Press, 2007).

[3] F. Han, A Modern Course in University Physics (World Scientific, 2017).