Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each (Al-27 = 26.981538 amu, Am-241 = 241.056822 amu, He-4 = 4.002603 amu, Np-237 = 237.048166 amu, P-30 = 29.981801 amu, S-32 = 31.972071 amu, and Si-29 = 28.976495 amu).
b. ³²₁₆S + ______ → ²⁹₁₄Si + ⁴₂He
c. ²⁴¹₉₅Am → ²³⁷₉₃Np + _____

Verified step by step guidance

1. Identify the missing particle in each nuclear equation by balancing the atomic and mass numbers on both sides of the equation.
2. For equation b: \( ^{32}_{16}\text{S} + \text{?} \rightarrow ^{29}_{14}\text{Si} + ^{4}_{2}\text{He} \), calculate the missing particle's atomic and mass numbers by subtracting the known products from the reactant.
3. For equation c: \( ^{241}_{95}\text{Am} \rightarrow ^{237}_{93}\text{Np} + \text{?} \), calculate the missing particle's atomic and mass numbers by subtracting the known product from the reactant.
4. Calculate the mass defect for each reaction by finding the difference in mass between the reactants and products using the given atomic masses.
5. Use Einstein's equation \( E = \Delta m c^2 \) to calculate the energy change, where \( \Delta m \) is the mass defect in kg and \( c \) is the speed of light (\( 3.00 \times 10^8 \text{ m/s} \)). Convert the energy change to J/mol by multiplying by Avogadro's number (\( 6.022 \times 10^{23} \text{ mol}^{-1} \)).

Key Concepts

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and can result in the transformation of one element into another. They are characterized by the conservation of mass and energy, where the total mass and energy before and after the reaction remain constant. Understanding the types of nuclear reactions, such as alpha decay, beta decay, and fusion, is essential for completing nuclear equations.

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², indicates that mass can be converted into energy and vice versa. In nuclear reactions, the mass of the reactants may differ from the mass of the products, leading to a release or absorption of energy. This concept is crucial for calculating the energy change associated with nuclear reactions, as it allows for the determination of energy in joules per mole of reactant.

Atomic Mass Units (amu)

Atomic mass units (amu) are a standard unit of mass used to express atomic and molecular weights. One amu is defined as one twelfth of the mass of a carbon-12 atom. In nuclear equations, the precise atomic masses of the isotopes involved are necessary for calculating the energy changes, as they help determine the mass defect and the energy released or absorbed during the reaction.