Question

Write balanced nuclear equations for the bombardment of (a) U-238 with a nucleus to produce Fm-249 and five neutrons. (b) Al-26 with an alpha particle to produce P-30. (c) Cu-63 with a nucleus producing \(\mathrm{Zn}-63\) and a neutron. (d) Al-27 with deuterium \(\left({ }_{1}^{2} \mathrm{H}\right)\) to produce an alpha particle and another nucleus.

Short answer

Based on the given step by step solution, create a short answer for each reaction: (a) In the given nuclear reaction, Uranium-238 is bombarded with Oxygen-11 to produce Fermium-249 and five neutrons. The balanced nuclear equation is: \({}_{92}^{238}\mathrm{U} + {}_{8}^{11}\mathrm{O} \rightarrow {}_{100}^{249}\mathrm{Fm} + 5{}_{0}^{1}\mathrm{n}\) (b) In the given nuclear reaction, Aluminum-26 reacts with an alpha particle to produce Phosphorus-30. The balanced nuclear equation is: \({}_{13}^{26}\mathrm{Al} + {}_{2}^{4}\mathrm{He} \rightarrow {}_{15}^{30}\mathrm{P}\) (c) In the given nuclear reaction, Copper-63 reacts with Hydrogen-1 to produce Zinc-63 and a neutron. The balanced nuclear equation is: \({}_{29}^{63}\mathrm{Cu} + {}_{1}^{1}\mathrm{H} \rightarrow {}_{30}^{63}\mathrm{Zn} + {}_{0}^{1}\mathrm{n}\) (d) In the given nuclear reaction, Aluminum-27 reacts with deuterium to produce an alpha particle and Magnesium-25. The balanced nuclear equation is: \({}_{13}^{27}\mathrm{Al} + {}_{1}^{2}\mathrm{H} \rightarrow {}_{2}^{4}\mathrm{He} + {}_{12}^{25}\mathrm{Mg}\)

Step-by-step solution

(a) U-238 with a nucleus to produce Fm-249 and five neutrons

In this reaction, we have the bombardment of Uranium-238 with a nucleus to produce Fermium-249 and five neutrons. We need to identify the nucleus and write down the balanced nuclear equation. 1. U-238 (with A=238 and Z=92) is bombarded with a nucleus. Let the nucleus be represented as X with A=X and Z=Y. 2. The reaction produces Fm-249 (with A=249 and Z=100) and five neutrons (with A=1 and Z=0 each). 3. Write down the nuclear equation and balance the mass numbers (A) and atomic numbers (Z) on both sides. U-238 + X -> Fm-249 + 5n 238 + X = 249 => X=11 92+ Y = 100 => Y=8 Since X=11 and Y=8, the nucleus is Oxygen-11 (O-11). The balanced nuclear equation for this reaction is: \({}_{92}^{238}\mathrm{U} + {}_{8}^{11}\mathrm{O} \rightarrow {}_{100}^{249}\mathrm{Fm} + 5{}_{0}^{1}\mathrm{n}\)

(b) Al-26 with an alpha particle to produce P-30

In this reaction, Aluminum-26 reacts with an alpha particle to produce Phosphorus-30. Let's write the balanced nuclear equation for this reaction. 1. Al-26 (A=26, Z=13) reacts with an alpha particle, which is a Helium-4 nucleus (A=4, Z=2). 2. The reaction produces P-30 (A=30, Z=15). 3. Write down the nuclear equation and balance the mass numbers (A) and atomic numbers (Z) on both sides. Al-26 + He-4 -> P-30 \({}_{13}^{26}\mathrm{Al} + {}_{2}^{4}\mathrm{He} \rightarrow {}_{15}^{30}\mathrm{P}\)

(c) Cu-63 with a nucleus producing Zn-63 and a neutron

In this reaction, Copper-63 reacts with a nucleus to produce Zinc-63 and a neutron. Let's write the balanced nuclear equation for this reaction. 1. Cu-63 (A=63, Z=29) reacts with a nucleus. Let the nucleus be represented as X with A=X and Z=Y. 2. The reaction produces Zn-63 (A=63, Z=30) and a neutron (A=1, Z=0). 3. Write down the nuclear equation and balance the mass numbers (A) and atomic numbers (Z) on both sides. Cu-63 + X -> Zn-63 + n 63 + X = 63 + 1 => X=1 29 + Y = 30 => Y=1 Since X=1 and Y=1, the nucleus is Hydrogen-1 (H-1). The balanced nuclear equation for this reaction is: \({}_{29}^{63}\mathrm{Cu} + {}_{1}^{1}\mathrm{H} \rightarrow {}_{30}^{63}\mathrm{Zn} + {}_{0}^{1}\mathrm{n}\)

(d) Al-27 with deuterium to produce an alpha particle and another nucleus

In this reaction, Aluminum-27 reacts with deuterium to produce an alpha particle and another nucleus. Let's write the balanced nuclear equation for this reaction. 1. Al-27 (A=27, Z=13) reacts with deuterium, which is Hydrogen-2 (A=2, Z=1). 2. The reaction produces an alpha particle (A=4, Z=2) and another nucleus. Let the nucleus be represented as X with A=X and Z=Y. 3. Write down the nuclear equation and balance the mass numbers (A) and atomic numbers (Z) on both sides. Al-27 + H-2 -> He-4 + X 27 + 2 = 4 + X => X=25 13 + 1 = 2 + Y => Y=12 Since X=25 and Y=12, the nucleus produced is Magnesium-25 (Mg-25). The balanced nuclear equation for this reaction is: \({}_{13}^{27}\mathrm{Al} + {}_{1}^{2}\mathrm{H} \rightarrow {}_{2}^{4}\mathrm{He} + {}_{12}^{25}\mathrm{Mg}\)

Key concepts

Nuclear Reaction

In the fascinating world of nuclear chemistry, a nuclear reaction is a process where two atomic nuclei or a nucleus and a subatomic particle collide to produce new elements or isotopes. These reactions are driven by forces that operate at the nucleus’s scale and can release or consume large amounts of energy. For example, when Uranium-238 is bombarded with an Oxygen-11 nucleus in a high-energy collision, it forms the element Fermium-249 while releasing five neutrons. It is a showcase of how nuclear reactions are pivotal for creating elements that do not naturally exist on Earth and for understanding fundamental physics principles.

By delving deep into these reactions, students not only grasp the mechanisms of element formation but also unlock understanding of the principles behind nuclear energy and its applications, from medical treatments to energy generation. Always ensure that the mass number and atomic number are balanced on both sides of the equation, reflecting the law of conservation of mass and energy.

Radioactive Decay

Moving on to a closely related phenomenon, radioactive decay is a form of a nuclear reaction where an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This natural process can transform one chemical element into another and is characterized by its spontaneity. Unlike nucleosynthesis in stars or human-made nuclear reactions that often involve acceleration of particles, radioactive decay happens at random and at a constant statistical rate for each isotope, described by its half-life.

Understanding radioactive decay is crucial for fields such as archeology for carbon dating, medicine for diagnostic and therapeutic techniques, and for managing nuclear waste safely. It highlights the importance of time and stability in nuclear chemistry, with extensive applications in both scientific research and everyday life.

Nuclear Chemistry

Nuclear chemistry is the sub-discipline of chemistry that deals with changes in the nucleus of elements. It encompasses a variety of processes, including both nuclear reactions and radioactive decay as illustrated by our textbook nuclear equations examples. Students journey through this realm by learning about the manipulation and transmutation of elements, radioactivity and its detection, as well as the intricacies of fission, fusion, and other nuclear processes.

As they dive deeper into nuclear chemistry, students gain valuable insights into the generation of energy from nuclear power plants, the development of new methods for diagnosing and treating diseases, and the impact of radioactive elements on the environment. It is also a field that continuously poses challenging questions and provides cutting-edge research opportunities, bridging physics and chemistry in a unique way.

Isotopes

Lastly, we come to isotopes, which are variants of a particular chemical element that have the same number of protons, hence the same atomic number, but different numbers of neutrons. This difference in neutron count gives rise to varied mass numbers, which in turn can influence the stability of the nucleus. Some isotopes are stable, while others are radioactive and can participate in radioactive decay, emitting particles until they reach a more stable state.

Isotopes have profound roles in nuclear chemistry: they can serve as tracers in biochemical experiments, provide a basis for radiometric dating techniques to determine the ages of rocks and fossils, and even form the backbone of nuclear medicine. Whether stable or radioactive, isotopes and their behaviors are central to grasping the complexities and applications of nuclear chemistry.