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) ⁶₃Li + ⁵⁶₂₈Ni → ?
(b) ⁴⁰₂₀Ca + ²⁴⁸₉₆Cm → ¹⁴⁷₆₂Sm + ?
(c) ⁸⁸₃₈Sr + ⁸⁴₃₆Kr → ¹¹⁶₄₆Pd + ?
(d) ⁴⁰₂₀Ca + ²³⁸₉₂U → ⁷⁰₃₀Zn + 4 ¹₀n + 2 ?

Verified step by step guidance

1. Identify the reactants and products in the nuclear reaction: \(^{40}_{20}\text{Ca} + ^{248}_{96}\text{Cm} \rightarrow ^{147}_{62}\text{Sm} + ?\).
2. Apply the law of conservation of mass number (A): The sum of mass numbers of reactants should equal the sum of mass numbers of products.
3. Apply the law of conservation of atomic number (Z): The sum of atomic numbers of reactants should equal the sum of atomic numbers of products.
4. Calculate the missing mass number by subtracting the known mass numbers from the total mass number of reactants.
5. Calculate the missing atomic number by subtracting the known atomic numbers from the total atomic number of reactants.

Key Concepts

Nuclear Reactions

Nuclear reactions involve the transformation of atomic nuclei through processes such as fusion, fission, or bombardment. In these reactions, the identities and numbers of the particles involved change, leading to the formation of new elements or isotopes. Understanding the conservation of mass and charge is crucial for balancing these reactions.

Heavy-Ion Bombardment

Heavy-ion bombardment is a technique used in nuclear physics where heavy ions, such as those from elements like calcium or curium, are accelerated and directed at target nuclei. This process can induce nuclear reactions that create new isotopes or elements not found in nature. The energy of the bombardment is significant for overcoming the repulsive forces between positively charged nuclei.

Balancing Nuclear Reactions

Balancing nuclear reactions requires ensuring that both the mass number and atomic number are conserved. This means that the total number of protons and neutrons before the reaction must equal the total after the reaction. In the given reaction, identifying the missing product involves calculating the difference in mass and atomic numbers between the reactants and products.