The Law of Conservation of Matter states that matter, or mass, cannot be created or destroyed within a closed system. This principle is fundamental to understanding standard chemical reactions, where the mass of the starting materials always equals the mass of the products. In nuclear reactions, the law remains a powerful tool, though its application shifts due to massive energy changes. Nuclear equations, which represent changes within the atomic nucleus, rely on a modified conservation concept to ensure the process is physically sound.
The Foundation of Conservation
In typical chemical reactions, the conservation of mass is straightforward because the atoms remain intact and are simply rearranged into new molecules. Nuclear reactions involve changes to the nucleus, where small amounts of mass are converted into enormous amounts of energy, as described by Einstein’s equation E=mc^2. This conversion means the total mass of the products is measurably less than the total mass of the reactants, a difference known as the mass defect.
For balancing nuclear equations, two specific quantities are conserved across the reaction: the total number of nucleons and the total electric charge. Nucleons are the protons and neutrons found in the nucleus, and their total count is represented by the mass number. The total electric charge is determined by the number of protons, which is the atomic number.
The conservation of the mass number (total protons and neutrons) and the atomic number (total protons) is necessary for accurately describing any nuclear change. This simplified application, focused on the count of subatomic particles, allows scientists to track the transformation of one element into another, a process known as transmutation.
Understanding Nuclear Notation
To write nuclear equations, a specific notation is used to represent isotopes and the subatomic particles involved in the reaction. Every nucleus is symbolized by its chemical element symbol, with two numbers placed to the left of the symbol. The mass number is written as a superscript in the upper left position, and this number is the sum of protons and neutrons in the nucleus. The atomic number is written as a subscript in the lower left position, representing the number of protons that uniquely defines the element. For example, in the notation for uranium-238, \(^{238}_{92}\text{U}\), the mass number is 238, and the atomic number is 92.
Particles involved in a reaction are also represented with this same notation system. An alpha particle (a helium nucleus) is written as \(^{4}_{2}\text{He}\), having a mass number of 4 and an atomic number of 2. A beta particle (an electron) is written as \(^{0}_{-1}\text{e}\), with a mass number of 0 and a charge of -1. A neutron is represented as \(^{1}_{0}\text{n}\), signifying a mass number of 1 and a charge of 0.
Writing Balanced Nuclear Equations
The application of the conservation law in nuclear equations involves a straightforward algebraic process. A nuclear equation is balanced when the sum of the mass numbers (superscripts) on the reactant side equals the sum of the mass numbers on the product side. Simultaneously, the sum of the atomic numbers (subscripts) on the reactant side must equal the sum of the atomic numbers on the product side. This twin requirement ensures the conservation of both nucleons and charge.
Consider the alpha decay of uranium-238, a common example of a nuclear transformation. The decay is written as \(^{238}_{92}\text{U} \rightarrow ^{\text{A}}_{\text{Z}}\text{X} + ^{4}_{2}\text{He}\), where X is the unknown daughter nucleus. To solve for the mass number A, one sets up an equation for the superscripts: \(238 = A + 4\), which reveals that A = 234. Next, the atomic number Z is found by setting up an equation for the subscripts: \(92 = Z + 2\), which shows that Z = 90, identifying the product as thorium (Th).