Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each (Be-9 = 9.012182 amu, Bi-209 = 208.980384 amu, He-4 = 4.002603 amu, Li-6 = 6.015122 amu, Ni-64 = 63.927969 amu, Rg-272 = 272.1535 amu, Ta-179 = 178.94593 amu, and W-179 = 178.94707 amu). a. _____ + ⁹₄Be → ⁶₃Li + ⁴₂He

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Identify the missing reactant in the nuclear equation. The sum of atomic numbers and mass numbers on both sides of the equation must be equal.

The given equation is: X + ^9_4Be → ^6_3Li + ^4_2He. Calculate the atomic number and mass number for the missing reactant X.

The atomic number of X is calculated as: 3 (Li) + 2 (He) - 4 (Be) = 1. The mass number of X is: 6 (Li) + 4 (He) - 9 (Be) = 1.

The missing reactant is ^1_1H (a proton). The complete equation is: ^1_1H + ^9_4Be → ^6_3Li + ^4_2He.

Calculate the energy change using the mass defect and Einstein's equation, E = Δmc^2. Find the mass defect by subtracting the total mass of products from the total mass of reactants, convert to kg, and multiply by c^2 (speed of light squared). Finally, convert the energy from J to J/mol.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and can result in the transformation of one element into another. These reactions are characterized by the conservation of mass and charge, where the total number of nucleons (protons and neutrons) remains constant. Understanding the types of nuclear reactions, such as fusion and fission, is essential for completing nuclear equations and predicting the products formed.

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, a small amount of mass is often lost and converted into energy, which can be calculated to determine the energy change associated with the reaction. This concept is crucial for calculating the energy change in nuclear equations, as it allows for the quantification of energy released or absorbed.

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 masses of reactants and products are often given in amu, and understanding how to convert these values into energy (in J/mol) is vital for calculating the energy changes associated with nuclear reactions.

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Related Practice

Textbook Question

Write the nuclear equation for the most likely mode of decay for each unstable nuclide. a. Ru-114 c. Zn-58 d. Ne-31

Textbook Question

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).

a. ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ____

Textbook Question

Suppose a patient is given 1.55 mg of I-131, a beta emitter with a half-life of 8.0 days. Assuming that none of the I-131 is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?