Question

Nuclear scientists have synthesized approximately 1600 nuclei not known in nature. More might be discovered with heavy-ion bombardment using high-energy particle accelerators. Complete and balance the following reactions, which involve heavy-ion bombardments: \begin{equation} (a) \stackrel{6}{3} \mathrm{Li}+\stackrel{56}{28} \mathrm{Ni} \longrightarrow ? \end{equation}\begin{equation}(b) \stackrel{40}{20} \mathrm{Ca}+\stackrel {248}{96} \mathrm{Cm} \longrightarrow \stackrel{147}{62} \mathrm{Sm} + ? \end{equation}\begin{equation}(c) \stackrel{88}{38} \mathrm{Sr}+\stackrel{84}{36} \mathrm{Kr} \longrightarrow \stackrel{116}{46} \mathrm{Pd} + ?\end{equation}\begin{equation} (d)\stackrel{40}{20} \mathrm{Ca}+\stackrel{238}{92} \mathrm{U} \longrightarrow \stackrel{70}{30} \mathrm{Zn}+4 \stackrel{1}{0}\mathrm{n}+2 ?\end{equation}

Short answer

The short answers for the given reactions are: (a) \[ \stackrel{6}{3} \mathrm{Li}+\stackrel{56}{28} \mathrm{Ni} \longrightarrow \stackrel{90}{31}\mathrm{X} \] (b) \[ \stackrel{40}{20} \mathrm{Ca}+\stackrel{248}{96} \mathrm{Cm} \longrightarrow \stackrel{147}{62} \mathrm{Sm} + \stackrel{185}{54} \mathrm{X} \] (c) \[ \stackrel{88}{38} \mathrm{Sr}+\stackrel{84}{36} \mathrm{Kr} \longrightarrow \stackrel{116}{46} \mathrm{Pd} + \stackrel{56}{28} \mathrm{X} \] (d) \[ \stackrel{40}{20} \mathrm{Ca}+\stackrel{238}{92} \mathrm{U} \longrightarrow \stackrel{70}{30} \mathrm{Zn}+4 \stackrel{1}{0}\mathrm{n}+2 \stackrel{102}{41} \mathrm{X} \]

Step-by-step solution

(a) Completing and balancing the reaction

For the first reaction, we can calculate the total number of protons and neutrons and keep them conserved in the final product. The total number of protons in the reactants is 3+28=31 and the total number of neutrons is 3+28=59. So the product of the reaction is \( \stackrel{90}{31} \mathrm{X} \), where X is an unknown element. The balanced reaction would be: \[ \stackrel{6}{3} \mathrm{Li}+\stackrel{56}{28} \mathrm{Ni} \longrightarrow \stackrel{90}{31}\mathrm{X} \]

(b) Completing and balancing the reaction

In this reaction, we need to find the missing product. The total number of protons in the reactants is 20+96=116 and the total number of neutrons is 20+152=172. The product \( \stackrel{147}{62} \mathrm{Sm} \) has 62 protons and 85 neutrons. We can find the missing product's protons and neutrons by looking at the remaining values. The missing product has 116-62=54 protons and 172-85=87 neutrons, which makes it \( \stackrel{185}{54} \mathrm{X} \), for an unknown element X. The balanced reaction would be: \[ \stackrel{40}{20} \mathrm{Ca}+\stackrel{248}{96} \mathrm{Cm} \longrightarrow \stackrel{147}{62} \mathrm{Sm} + \stackrel{185}{54} \mathrm{X} \]

(c) Completing and balancing the reaction

For this reaction, we again need to find the missing product. The total number of protons in the reactants is 38+36=74 and the total number of neutrons is 50+48=98. The product \( \stackrel{116}{46} \mathrm{Pd} \) has 46 protons and 70 neutrons. We can find the missing product's protons and neutrons by looking at the remaining values. The missing product has 74-46=28 protons and 98-70=28 neutrons, which makes it \( \stackrel{56}{28} \mathrm{X} \), for an unknown element X. The balanced reaction would be: \[ \stackrel{88}{38} \mathrm{Sr}+\stackrel{84}{36} \mathrm{Kr} \longrightarrow \stackrel{116}{46} \mathrm{Pd} + \stackrel{56}{28} \mathrm{X} \]

(d) Completing and balancing the reaction

In this reaction, we have to find the missing 2 products. The total number of protons in the reactants is 20+92=112, and the total number of neutrons is 20+146=166. The known products are \( \stackrel{70}{30} \mathrm{Zn} \) with 30 protons and 40 neutrons, and 4 neutrons (4\( \stackrel{1}{0}\mathrm{n}\)). We have remaining 112-30=82 protons and 166-40-4=122 neutrons. These are distributed among 2 products, therefore each of them would have 41 protons and 61 neutrons, which makes them \( \stackrel{102}{41} \mathrm{X} \), for an unknown element X. The balanced reaction would be: \[ \stackrel{40}{20} \mathrm{Ca}+\stackrel{238}{92} \mathrm{U} \longrightarrow \stackrel{70}{30} \mathrm{Zn}+4 \stackrel{1}{0}\mathrm{n}+2 \stackrel{102}{41} \mathrm{X} \]

Key concepts

Heavy-Ion Bombardment

The term 'heavy-ion bombardment' refers to a process used in nuclear physics to explore the properties of atomic nuclei. This technique involves accelerating ions, which are atoms that have lost or gained electrons and carry an electrical charge, to high speeds and smashing them into target nuclei. By using heavier ions, such as those from heavier elements like lead or uranium, scientists can produce a significant amount of energy upon impact, which can lead to the creation of new elements or isotopes that do not occur naturally.

This method is crucial in studying nuclear reactions and helping us to understand fundamental aspects of atomic structure and the forces that bind protons and neutrons in the nucleus. It also plays a vital role in synthesizing new elements, contributing to our knowledge about the limits of the periodic table.

Understanding the Force of Impact

When two heavy ions collide, the force of the impact is so intense that it can overcome the strong nuclear force bonding the protons and neutrons together in the nucleus. This results in the fusing of the nuclei to form a heavier nucleus or in some cases, breaking them apart in a process called spallation.

Particle Accelerators

Particle accelerators are sophisticated machines that use electromagnetic fields to propel charged particles, such as protons, electrons, or heavy ions, to high speeds - often close to the speed of light - and to contain them in well-defined beams. These accelerators come in various designs, including linear accelerators (linacs), cyclotrons, and synchrotrons.

They are extremely important tools in nuclear physics. Scientists use accelerators to provide the high-energy particles needed for heavy-ion bombardment. By doing so, particle accelerators enable physicists to delve into the subatomic world, probing the structure of atomic nuclei and generating conditions suitable for nuclear reactions and the synthesis of new nuclei.

From Medicine to Research

Apart from fundamental research in physics, particle accelerators have practical applications in medicine for treatments like radiation therapy for cancer patients and in industry for the inspection of materials and processes.

Nuclei Synthesis

Nuclei synthesis, often referred to as nucleosynthesis, is the process of creating new atomic nuclei from pre-existing nucleons (protons and neutrons). This process is fundamentally different from chemical processes that involve only the electron cloud of atoms and leads to the formation of different molecules.

There are several types of nucleosynthesis, including primordial (which took place shortly after the Big Bang), stellar (which happens within stars), and artificial (which is man-made, often achieved in laboratories). Heavy-ion bombardment in particle accelerators is a key method for artificial nucleosynthesis, helping scientists to create superheavy elements that expand our understanding of the universe's building blocks.

Pushing Boundaries in Laboratories

Laboratory nucleosynthesis has led to the discovery of many new elements, often found at the bottom of the periodic table. These elements are usually highly unstable and exist for only a fraction of a second before decaying into lighter elements.

Protons and Neutrons Conservation

The conservation of protons and neutrons, commonly known as the conservation of baryon number, is a fundamental principle in physics stating that the total number of protons and neutrons (baryons) in an isolated system remains constant throughout any physical process.

This principle is of particular importance when balancing nuclear reactions, where the total number of protons defines the element's identity, and the number of neutrons, along with protons, defines the isotope of that element. For a nuclear reaction to be balanced, the total number of protons and neutrons before the reaction must equal the total number after the reaction, adhering to the law of baryon conservation.

Deciphering Nuclear Equations

When balancing nuclear equations involving heavy-ion bombardment, such as those provided in the exercise, protons and neutrons are tracked to ensure the mass and atomic numbers are conserved. This allows for the final products to be accurately determined, as seen in the steps provided in the solution. This conservation governs the stability of the nucleus and the possible transformations it can undergo during nuclear reactions.