
A nuclear reaction is any process that changes the nucleus of an atom. Nuclear reactions may change one element into another or change one isotope into a different isotope of the same element. Because nuclear reactions involve the strong nuclear force, the energy is typically a millions times greater compared to chemical reactions. Chemical reactions rearrange shared electrons but do not change the nucleus.

Writing balanced nuclear reaction equations

Nuclear reactions can change an element into a different element by altering the number of protons and neutrons. Nuclear reactions are represented by nuclear reaction equations, just as chemical reactions are represented by chemical reaction equations. Every nuclear reaction equation has two parts: reactants and products. Consider the nuclear reaction that produces carbon14 in the atmosphere. In this nuclear reaction, a neutron interacts with nitrogen14 to produce carbon14 and a proton. The equation for this reaction is (27.3)  $$\begin{array}{ccc}\underset{\text{Reactants}}{\underbrace{{}_{0}{}^{1}n+{}_{7}{}^{14}N}}& \to & \underset{\text{Products}}{\underbrace{{}_{6}{}^{14}C+{}_{1}{}^{1}p}}\end{array}$$


A correct nuclear equation must show mass balance by having the mass numbers equal on both sides of the equation. First, this means that the total number of protons plus neutrons must be the same before the reaction and after the reaction. Second, the total charge before the reaction must equal the total charge afterward, which is the basic law of charge conservation. These two fundamental rules for balancing nuclear reaction equations can be used to determine an unknown element in a reaction.

Consider the incomplete reaction equation $${}_{0}{}^{1}\text{n}+{}_{92}{}^{235}\text{U}\to {}_{Z}{}^{A}\text{X}+{}_{38}{}^{94}\text{S}\text{r}+{}_{0}{}^{1}\text{n}+{}_{0}{}^{1}\text{n}$$ To find the unknown element X we start by applying the charge conservation (proton balance) rule:
92 = Z + 38 ⇒ Z = 54
From the periodic table we see that the element with atomic number 54 is xenon. Next we identify the xenon isotope by applying the mass balance rule:
1 + 235 = A + 94 + 1 + 1 ⇒ A = 140
So the unknown nucleus is xenon140 or ${}_{54}{}^{140}\text{X}\text{e}$. The complete reaction is $${}_{0}{}^{1}\text{n}+{}_{92}{}^{235}\text{U}\to {}_{54}{}^{140}\text{X}\text{e}+{}_{38}{}^{94}\text{S}\text{r}+{}_{0}{}^{1}\text{n}+{}_{0}{}^{1}\text{n}$$

In a 1917 experiment, Rutherford bombarded a nitrogen14 nucleus with a helium4 nucleus (an alpha particle), causing the nitrogen atom to change to a different element and producing a proton. What was the resulting isotope of his reaction?

Answer: The resulting isotope is oxygen17. Asked: element that is the product of the nuclear reaction Given: particles before the reaction: helium4 and nitrogen14; atomic mass numbers before the reaction: helium has A = 4 and nitrogen has A = 14; particles after the reaction: proton and an unknown isotope Relationships: A = Z + N Solution: First, determine the atomic mass number of all the particles. Two are already given explicitly (helium4 and nitrogen14). The proton’s atomic mass number is A = 1. Look up the atomic number for all the particles: For He, Z = 2; for N, Z = 7; and for the proton, Z = 1. Write down the nuclear reaction equation: $${}_{2}{}^{4}\text{H}\text{e}+{}_{7}{}^{14}\text{N}\to {}_{Z}{}^{A}\text{?}\text{}+{}_{1}{}^{1}\text{p}$$
 The total number of nucleons, A, must remain the same, so the mystery isotope has A = 17. The total charge must be the same on both sides of the equation, so the mystery isotope must have Z = 8. Look up Z = 8 on the periodic table and we see that the mystery element is oxygen, so the isotope is oxygen17.
