Problem 30 - Chemistry: The Central Science

Question

Write balanced equations for each of the following nuclear reactions: (a) \({ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma)^{239} \mathrm{G}_{2} \mathrm{U}\), (b) \({ }_{7}^{14} \mathrm{~N}(\mathrm{p}, \alpha)^{11}{\underline{\phantom{xx}}}_{6} \mathrm{C}\), (c) \({ }^{18} \mathrm{O}(\mathrm{n}, \beta)^{1} \mathrm{~g} \mathrm{~F}\).

Step-by-Step Solution

Answer

The balanced equations for the given nuclear reactions are: (a) \({}_{92}^{238}\mathrm{U} + \mathrm{n} \rightarrow {}_{92}^{239}\mathrm{U}\) (b) \({}_{7}^{14}\mathrm{N} + \mathrm{p} \rightarrow {}_{4}^4\alpha + {}_{6}^{11}\mathrm{C}\) (c) \({}_{8}^{18}\mathrm{O} + \mathrm{n} \rightarrow {}_{-1}^{0}\beta + {}_{9}^{18}\mathrm{F}\)

Step 1: Reaction (a) Balancing

In this reaction, a uranium-238 nucleus absorbs a neutron and becomes uranium-239. Let's balance the equation: Reactants: - Uranium-238 nucleus: has 92 protons and 238 - 92 = 146 neutrons - Neutron: has 1 neutron Products: - Uranium-239 nucleus: has 92 protons and 239 - 92 = 147 neutrons Since the number of protons and neutrons on both sides remains the same, the balanced equation is: \({}_{92}^{238}\mathrm{U} + \mathrm{n} \rightarrow {}_{92}^{239}\mathrm{U}\)

Step 2: Reaction (b) Balancing

In this reaction, a nitrogen-14 nucleus absorbs a proton and releases an alpha particle, becoming carbon-11. Let's balance the equation: Reactants: - Nitrogen-14 nucleus: has 7 protons and 14 - 7 = 7 neutrons - Proton: has 1 proton Products: - Alpha particle: has 2 protons and 4 - 2 = 2 neutrons - Carbon-11 nucleus: has 6 protons and 11 - 6 = 5 neutrons Since the number of protons and neutrons on both sides remains the same, the balanced equation is: \({}_{7}^{14}\mathrm{N} + \mathrm{p} \rightarrow {}_{4}^4\alpha + {}_{6}^{11}\mathrm{C}\)

Step 3: Reaction (c) Balancing

In this reaction, an oxygen-18 nucleus absorbs a neutron and undergoes beta decay, becoming fluorine-18. Let's balance the equation: Reactants: - Oxygen-18 nucleus: has 8 protons and 18 - 8 = 10 neutrons - Neutron: has 1 neutron Products: - Beta particle: has -1 proton (it's an electron) - Fluorine-18 nucleus: has 9 protons and 18 - 9 = 9 neutrons Since the number of protons and neutrons on both sides remains the same, the balanced equation is: \({}_{8}^{18}\mathrm{O} + \mathrm{n} \rightarrow {}_{-1}^{0}\beta + {}_{9}^{18}\mathrm{F}\)

Key Concepts

Nuclear Chemistry

Nuclear chemistry involves the study of changes that occur within the nuclei of atoms. These changes can lead to the transmutation of elements, as the number of protons within a nucleus (which defines an element's identity) can change. Nuclear reactions differ from chemical reactions because they involve the nucleus, as opposed to electrons, and result in changes in an atom's atomic number or mass number.

Naturally occurring nuclear reactions include radioactive decay, where unstable isotopes (nuclides) spontaneously transform into more stable forms by emitting particles or radiation. These processes are integral to many phenomena, such as the heat generation in stars and the carbon dating of archeological artifacts. Understanding nuclear reactions not only explains these natural processes but is also crucial for practical applications like energy production in nuclear reactors and the development of medical imaging and cancer treatments.

Radioactive Decay

Radioactive decay is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. There are several types of radioactive decay, including alpha decay (emission of alpha particles), beta decay (conversion of a neutron into a proton or vice versa, accompanied by the emission of an electron or positron), and gamma decay (emission of high-energy photons).

The decay process leads to the transformation of the original (parent) nuclide into a different nuclide (daughter). This process changes the atomic number, and possibly the mass number, of the nuclide, thus altering its identity. Recognizing the type of decay and balancing the corresponding nuclear equations are essential for predicting the products of radioactive decay, which is vital for applications ranging from dating archaeological finds to calculating the dosage of radioisotopes in medical treatments.

Balancing Nuclear Equations

Balancing nuclear equations is analogous to balancing chemical equations, but instead of balancing atoms and charges, we are balancing nucleons, which include protons and neutrons, and energy. To balance a nuclear equation, one must ensure that both the atomic number (which represents the number of protons) and the mass number (the total number of protons and neutrons) are conserved. In simpler terms, the sum of the atomic numbers and mass numbers must be the same on both sides of the equation.

For example, in beta decay, a neutron is transformed into a proton while emitting an electron, often called a beta particle. Balancing this equation involves recognizing the electron as having an atomic number of -1, since it signifies the loss of a proton to the other side of the equation. Balancing the equations correctly is crucial for understanding the nature of the reactions and ensuring accurate predictions of the reaction products. The discipline exercised in the step by step solutions not only maintains the integrity of the elements involved in a reaction but also reflects the law of conservation of mass-energy that dictates the behavior of these nuclear phenomena.