Which represents a balanced nuclear equation?
${ }_{11}^{23} Na \longrightarrow{ }_{12}^{24} Mg +{ }_1^1 H$
${ }_{11}^{24} Na \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^0 e$
${ }_{13}^{24} Al \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^0 e$
${ }_{12}^{23} Mg \longrightarrow{ }_{12}^{24} Mg +{ }_0^1 n$
Answer (1)
Check if the mass numbers are balanced on both sides of each equation.
Check if the atomic numbers are balanced on both sides of each equation.
Identify the equation where both mass numbers and atomic numbers are balanced.
The balanced nuclear equation is 11 24 N a ⟶ 12 24 M g + − 1 0 e .
Explanation
Understanding Balanced Nuclear Equations We need to determine which of the given nuclear equations is balanced. A balanced nuclear equation must have the sum of the mass numbers (superscripts) and the sum of the atomic numbers (subscripts) the same on both sides of the equation.
Analyzing Each Equation Let's analyze each equation:
Equation 1: 11 23 N a ⟶ 12 24 M g + 1 1 H Mass numbers: Left side: 23, Right side: 24 + 1 = 25. Not balanced. Atomic numbers: Left side: 11, Right side: 12 + 1 = 13. Not balanced.
Equation 2: 11 24 N a ⟶ 12 24 M g + − 1 0 e Mass numbers: Left side: 24, Right side: 24 + 0 = 24. Balanced. Atomic numbers: Left side: 11, Right side: 12 + (-1) = 11. Balanced.
Equation 3: 13 24 A l ⟶ 12 24 M g + − 1 0 e Mass numbers: Left side: 24, Right side: 24 + 0 = 24. Balanced. Atomic numbers: Left side: 13, Right side: 12 + (-1) = 11. Not balanced.
Equation 4: 12 23 M g ⟶ 12 24 M g + 0 1 n Mass numbers: Left side: 23, Right side: 24 + 1 = 25. Not balanced. Atomic numbers: Left side: 12, Right side: 12 + 0 = 12. Balanced.
Conclusion From the analysis above, only the second equation, 11 24 N a ⟶ 12 24 M g + − 1 0 e , has both mass numbers and atomic numbers balanced on both sides.
Examples
Nuclear equations are used in various fields, such as nuclear medicine for diagnostic imaging and cancer treatment, and in nuclear power plants for energy production. Balancing nuclear equations ensures that the number of protons and neutrons is conserved, which is crucial for predicting the products and energy released in nuclear reactions. For instance, in positron emission tomography (PET) scans, radioactive isotopes that undergo positron emission are used. A balanced nuclear equation helps to track the transformation of these isotopes and the resulting particles, ensuring accurate imaging and safe procedures.
