Problem 76 - Chemistry: The Central Science in SI Units, Global Edition

Question

Nuclear scientists have synthesized new elements and isotopes, which are not known in nature using heavy-ion bombardment techniques in high-energy particle accelerators. Complete and balance the following reactions: (a) \({ }_{6}^{12} \mathrm{C}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+{ }_{2}^{4} \mathrm{He}\) (b) \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow\) ? (c) \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow ?\) (d) \({ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+4{ }_{0}^{1} \mathrm{n}\)

Step-by-Step Solution

Answer

(a) \({ }_{6}^{12} \mathrm{C}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{10}^{20}\mathrm{Ne}+{ }_{2}^{4} \mathrm{He}\) (b) \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow { }_{31}^{69}\mathrm{Ga}\) (c) \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow { }_{103}^{262}\mathrm{Lr}\) (d) \({ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{98}^{246}\mathrm{Cf}+4{ }_{0}^{1} \mathrm{n}\)

Step 1: Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (6 + 6 = ? + 2), so the unknown atomic number is 10.

Step 2: Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (12 + 12 = ? + 4), so the unknown mass number is 20. Therefore, the complete and balanced reaction is: \({ }_{6}^{12} \mathrm{C}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{10}^{20}\mathrm{Ne}+{ }_{2}^{4} \mathrm{He}\) (b) For the second reaction: \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow\) ?

Step 1: Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (3 + 28 = ?), so the unknown atomic number is 31.

Step 2: Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (6 + 63 = ?), so the unknown mass number is 69. Therefore, the complete and balanced reaction is: \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow { }_{31}^{69}\mathrm{Ga}\) (c) For the third reaction: \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow ?\)

Step 1: Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (98 + 5 = ?), so the unknown atomic number is 103.

Step 2: Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (252 + 10 = ?), so the unknown mass number is 262. Therefore, the complete and balanced reaction is: \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow { }_{103}^{262}\mathrm{Lr}\) (d) For the fourth reaction: \({ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+4{ }_{0}^{1} \mathrm{n}\)

Step 1: Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (92 + 6 = ? + 0), so the unknown atomic number is 98.

Step 2: Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (238 + 12 = ? + 4), so the unknown mass number is 246. Therefore, the complete and balanced reaction is: \({ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{98}^{246}\mathrm{Cf}+4{ }_{0}^{1} \mathrm{n}\)

Key Concepts

Heavy-Ion Bombardment

Heavy-ion bombardment is a fascinating method used by nuclear scientists to create new elements and isotopes. This process involves accelerating heavy ions, which are atoms with a significant atomic number, to high speeds and directing them onto target nuclei. When these ions collide with a target, they can induce nuclear reactions that result in the formation of new and sometimes previously unknown elements.
This technique allows scientists to synthesize elements that are not naturally occurring on Earth and has been instrumental in expanding the periodic table.

• Used to discover new elements
• Involves high-speed collisions
• Leads to nuclear reactions

Heavy-ion bombardment is not only a key technique in research but also helps to improve our understanding of the fundamental structure and behavior of atomic nuclei.

Particle Accelerators

Particle accelerators are essential tools in modern nuclear chemistry. These sophisticated machines accelerate charged particles, such as protons or heavy ions, to nearly the speed of light, allowing them to collide with target atoms with great energy. The result of such collisions can lead to significant discoveries in nuclear physics.

• Composed of long, straight or circular tunnels where particles are accelerated
• Help in simulating conditions required for nuclear reactions
• Support research into the properties of subatomic particles

Particle accelerators have greatly advanced our understanding of the basic forces and particles of matter and continue to be a mainstay in many groundbreaking experiments in nuclear chemistry.

Conservation of Atomic Numbers

In nuclear reactions, the conservation of atomic numbers is a fundamental principle. It states that the total number of protons, or atomic numbers, must be the same before and after a nuclear reaction. This principle is crucial for correctly balancing nuclear equations. For example, when calculating a reaction involving two nuclei, if the atomic numbers are known for all but one component, scientists can solve for the unknown using this conservation law.
The equation for nuclear reactions takes this conservation into account:

• Atomic numbers of reactants sum to those of products
• Essential for correctly identifying the elements produced

Mastering the conservation of atomic numbers ensures that nuclear chemists can accurately track and predict the outcomes of complex nuclear processes.

Conservation of Mass Numbers

Just as with atomic numbers, the conservation of mass numbers is another critical aspect of nuclear chemistry. It requires that the sum of mass numbers (total number of protons and neutrons) in the reactants equals the sum in the products of a nuclear reaction. This conservation helps in predicting which nuclei will form during a reaction and allows chemists to balance nuclear equations.

• Sum of reactants' mass numbers equals that of products
• Vital for determining nuclear stability and decay processes

Conservation of mass numbers is integral to understanding nuclear reactions, allowing scientists to ensure that no mass is lost or gained unexpectedly, thereby maintaining the integrity of the nuclear equation.