- Recognize that nuclear reactions differ from chemical reactions because they involve the transmutation of elements, meaning the number of atoms of each element is not conserved.
- Recall the fundamental conservation laws for nuclear reactions: the conservation of total mass number and the conservation of total atomic number.
- Identify that matching the total mass number of the reactants and products is a necessary condition for a correctly written fission equation.
- Conclude that the correct answer is option (a). \(\boxed{\text{a}}\)
Explanation
- Analyzing Nuclear Reaction Principles
Nuclear reactions, including fission reactions, are governed by specific conservation laws that ensure physical consistency. Unlike chemical reactions, where the types of atoms remain unchanged, nuclear reactions involve the transformation of elements through the reorganization of protons and neutrons within the nucleus. Therefore, the number of atoms of each element is not conserved. Instead, we rely on the conservation of fundamental nuclear properties.
- Evaluating the Conservation Laws
In any nuclear reaction, two fundamental conservation laws must be satisfied:
- Conservation of Mass Number (the total number of nucleons, i.e., protons and neutrons): The sum of the mass numbers (A) of the reactants must equal the sum of the mass numbers (A) of the products.
- Conservation of Atomic Number (the total number of protons, i.e., charge): The sum of the atomic numbers (Z) of the reactants must equal the sum of the atomic numbers (Z) of the products.
Comparing these to the given options, option (a) explicitly states the conservation of total mass number, which is a requirement for a balanced nuclear equation. Options (b) and (c) describe conditions that do not represent these fundamental conservation laws.
- Selecting the Correct Criterion
Evaluating the provided options:
- Option (a) states the total mass number must be equal. This aligns with the principle of conservation of mass number.
- Option (b) mentions the conservation of the number of atoms of each element. This applies to chemical reactions, not nuclear reactions where element identities change.
- Option (c) suggests equating the mass number of products to the atomic number of products, which is physically meaningless for balancing an equation.
Therefore, the correct way to check the equation is to verify that the total mass number is balanced between reactants and products.
Examples
Understanding the balance of mass and atomic numbers in nuclear reactions is essential in fields like nuclear physics and power engineering. For example, when scientists design nuclear reactors, they must ensure the fission reactions of Uranium-235 are correctly balanced to track the release of neutrons and energy accurately. By applying conservation laws to the reaction \({}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \to {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3({}^{1}_{0}\text{n})\), they verify that both the mass number (\(235+1 = 141+92+3\)) and atomic number (\(92+0 = 56+36+0\)) remain constant, ensuring the reaction model is correct.