To solve the nuclear reaction given in the question, we need to analyze the reaction step by step, focusing on the conservation of nucleons (protons and neutrons) and charge. ### Given Reaction: \[ ^{23}_{11}\text{Na} + \text{Proton} \rightarrow ^{p}_{q}\text{X} + \text{alpha particle} \] ### Step 1: Identify the Components 1. **Sodium-23 (\(^{23}_{11}\text{Na}\))**: - Mass number (A) = 23 (total number of protons and neutrons) - Atomic number (Z) = 11 (number of protons) 2. **Proton**: - Mass number (A) = 1 - Atomic number (Z) = 1 3. **Alpha Particle**: - Mass number (A) = 4 (2 protons and 2 neutrons) - Atomic number (Z) = 2 ### Step 2: Conservation of Mass Number and Atomic Number In nuclear reactions, both the mass number and atomic number must be conserved. This means that the total mass number and total atomic number on the left side of the equation must equal those on the right side. #### Left Side: - Total Mass Number = \(23 + 1 = 24\) - Total Atomic Number = \(11 + 1 = 12\) #### Right Side: Let’s denote the mass number of the unknown nucleus \(X\) as \(p\) and its atomic number as \(q\). The alpha particle contributes \(4\) to the mass number and \(2\) to the atomic number. So, the right side can be expressed as: - Total Mass Number = \(p + 4\) - Total Atomic Number = \(q + 2\) ### Step 3: Set Up the Equations From the conservation laws, we can set up the following equations: 1. **For Mass Number**: \[ p + 4 = 24 \] Rearranging gives: \[ p = 24 - 4 = 20 \] 2. **For Atomic Number**: \[ q + 2 = 12 \] Rearranging gives: \[ q = 12 - 2 = 10 \] ### Step 4: Conclusion Thus, the values of \(p\) and \(q\) are: - \(p = 20\) - \(q = 10\) This means the correct answer is **C. 20 and 10**. ### Step 5: Explanation of Other Options - **Option A (10 and 20)**: This option suggests that the atomic number is 10 and the mass number is 20, which does not satisfy the conservation equations derived above. - **Option B (12 and 24)**: This option suggests an atomic number of 12 and a mass number of 24, which also does not satisfy the conservation equations. The atomic number would exceed the total available from the reactants. - **Option D (24 and 12)**: This option suggests a mass number of 24 and an atomic number of 12, which again does not satisfy the conservation equations. The mass number is too high, as it exceeds the total mass number available from the reactants. ### Summary - The reaction conserves both mass number and atomic number. - The mass number of the product nucleus \(X\) is calculated to be 20. - The atomic number of the product nucleus \(X\) is calculated to be 10. - The correct answer is **C. 20 and 10**. ### Revision Summary - Always check conservation of mass number and atomic number in nuclear reactions. - Identify the components of the reaction clearly (mass and atomic numbers). - Set up equations based on conservation laws to find unknowns. - Verify your answer by checking against the original reaction.