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: (a) \({ }_{3}^{6} \mathrm{Li}+{ }_{29}^{56} \mathrm{Ni} \rightarrow\) ? (b) \(_{20}^{40} \mathrm{Ca}+{ }_{96}^{248} \mathrm{Cm} \ldots{ }_{62}^{147} \mathrm{Sm}+?\) (c) \(_{38}^{88} \mathrm{Sr}+{ }_{36}^{84} \mathrm{Kr} \ldots{ }_{46} 116 \mathrm{Pd}+?\) (d) \({ }_{20}^{40} \mathrm{Ca}+{ }_{92}^{238} \mathrm{U} \cdots{ } \rightarrow \frac{70}{30} \mathrm{Zn}+4_{0}^{1} \mathrm{n}+2 ?\)

Short answer

The balanced nuclear reactions involving heavy-ion bombardments are as follows: (a) \(_{3}^{6} \mathrm{Li} +_{29}^{56} \mathrm{Ni} \rightarrow _{32}^{62} \mathrm{Ga}\) (b) \(_{20}^{40} \mathrm{Ca}+{ }_{96}^{248} \mathrm{Cm} \Rightarrow{ }_{62}^{147} \mathrm{Sm} + _{54}^{141}\mathrm{Xe}\) (c) \(_{38}^{88} \mathrm{Sr}+{ }_{36}^{84} \mathrm{Kr} \rightarrow{ }_{46}^{116} \mathrm{Pd} + _{28}^{56}\mathrm{Ni}\) (d) \(_{20}^{40} \mathrm{Ca}+{ }_{92}^{238} \mathrm{U} \rightarrow _{30}^{70} \mathrm{Zn} + 4_{0}^{1} \mathrm{n} + _{82}^{204} \mathrm{Pb}\)

Step-by-step solution

(a) Balancing the reaction

To balance a nuclear reaction, we need to make sure that the sum of the atomic numbers (subscript) and the sum of mass numbers (superscript) are equal on both sides of the reaction. In this case, we have: \(_{3}^{6} \mathrm{Li} + _{29}^{56} \mathrm{Ni} \rightarrow X\) First, let's sum the atomic numbers on the left-hand side: 3 + 29 = 32. Then, let's sum the mass numbers on the left-hand side: 6 + 56 = 62. So we need a nucleus that has an atomic number of 32 and a mass number of 62, which is Gallium: \(_{3}^{6} \mathrm{Li} + _{29}^{56} \mathrm{Ni} \rightarrow _{32}^{62} \mathrm{Ga}\)

(b) Balancing the reaction

We have the reaction: \(_{20}^{40} \mathrm{Ca}+{ }_{96}^{248} \mathrm{Cm} \Rightarrow{ }_{62}^{147} \mathrm{Sm} + X\) First, calculate the sum of atomic numbers on both sides: Left side: 20 + 96 = 116 Right side: 62 116 - 62 = 54 (The atomic number of X) Next, calculate the sum of mass numbers on both sides: Left side: 40 + 248 = 288 Right side: 147 288 - 147 = 141 (The mass number of X) So, X is: \(_{20}^{40} \mathrm{Ca}+{ }_{96}^{248} \mathrm{Cm} \Rightarrow{ }_{62}^{147} \mathrm{Sm} + _{54}^{141}\mathrm{Xe}\)

(c) Balancing the reaction

We have the reaction: \(_{38}^{88} \mathrm{Sr}+{ }_{36}^{84} \mathrm{Kr} \rightarrow{ }_{46}^{116} \mathrm{Pd} + X \) First, calculate the sum of atomic numbers on both sides: Left side: 38 + 36 = 74 Right side: 46 74 - 46 = 28 (The atomic number of X) Next, calculate the sum of mass numbers on both sides: Left side: 88 + 84 = 172 Right side: 116 172 - 116 = 56 (The mass number of X) So, X is: \(_{38}^{88} \mathrm{Sr}+{ }_{36}^{84} \mathrm{Kr} \rightarrow{ }_{46}^{116} \mathrm{Pd} + _{28}^{56}\mathrm{Ni}\)

(d) Balancing the reaction

We have the reaction: \(_{20}^{40} \mathrm{Ca}+{ }_{92}^{238} \mathrm{U} \rightarrow _{30}^{70} \mathrm{Zn} + 4_{0}^{1} \mathrm{n} + X \) First, calculate the sum of atomic numbers on both sides: Left side: 20 + 92 = 112 Right side: 30 Since there are 4 neutrons, we do not add them to the atomic number. So, 112 - 30 = 82 (The atomic number of X) Next, calculate the sum of mass numbers on both sides: Left side: 40 + 238 = 278 Right side: 70 + 4 (4 neutrons on the right side) 278 - 74 = 204 (The mass number of X) So, X is: \(_{20}^{40} \mathrm{Ca}+{ }_{92}^{238} \mathrm{U} \rightarrow _{30}^{70} \mathrm{Zn} + 4_{0}^{1} \mathrm{n} + _{82}^{204} \mathrm{Pb} \)

Key concepts

Heavy-Ion Bombardment

Heavy-ion bombardment is a technique used in nuclear physics to explore the structure of atomic nuclei and to synthesize new elements. It involves accelerating ions, which are atoms that have been stripped of electrons, to high energies before smashing them into a target material. The ions used are typically heavier than hydrogen or helium, hence the term 'heavy-ion'. When these high-energy ions strike the nuclei in the target, a variety of nuclear reactions can occur, including fusion, fission, and transmutation.

This process is a fundamental part of modern nuclear research, allowing scientists to create and study elements that do not occur naturally on Earth. For instance, in exercises (a) and (d) given in our problem, lithium-6 and calcium-40 are bombarded onto nickel-56 and uranium-238 respectively, resulting in new elements and shedding light on the properties of nuclei.

Atomic Number

The atomic number, often represented with the letter Z, is a fundamental property of an atom. It defines the number of protons in the nucleus of an atom, and as such, determines the chemical identity of the element. For example, all atoms with 1 proton are hydrogen atoms, and all atoms with 6 protons are carbon atoms, irrespective of the number of neutrons or electrons.

This is particularly crucial when balancing nuclear reactions, as the atomic number must be conserved. During heavy-ion bombardment, as protons are part of the nuclei participating in the reaction, the sum of atomic numbers before the reaction must equal the sum afterwards. This rule is followed in steps 1 to 4 of the exercise, ensuring the identities of the resulting elements are correctly identified.

Mass Number

The mass number, denoted by A, represents the total number of protons and neutrons in an atom's nucleus. While the atomic number distinguishes one element from another, the mass number helps distinguish between different isotopes of the same element. Isotopes have the same number of protons but differ in the number of neutrons they contain.

When nuclear reactions occur, such as in heavy-ion bombardment, not only must the atomic number be conserved, but also the mass number. This means the combined mass numbers of the reactant nuclei must equal the combined mass numbers of the product nuclei. In the provided solutions, using mass number conservation allows us to determine the second product of the reactions, which completes the process of balancing the nuclear equations.

Particle Accelerators

Particle accelerators are sophisticated machines designed to accelerate charged particles, such as ions, to high speeds, often close to the speed of light. These particles gain tremendous kinetic energy, which is crucial for investigating the structure of matter and carrying out various nuclear reactions, including heavy-ion bombardment.

There are several types of accelerators, including linear accelerators (linacs) and circular ones like synchrotrons and cyclotrons. These devices are not only used in fundamental nuclear physics research but also have practical applications in medical treatment, such as cancer radiotherapy, and in industrial processes. Within the realm of nuclear physics, particle accelerators are the tools that allow us to explore the uncharted territories of the periodic table by creating new elements and isotopes that can't be found in nature.