Write the balanced nuclear equation for the reaction represented by the diagram shown here. [Section 21.2]

Verified step by step guidance

1. Identify the initial and final nuclei in the diagram. The initial nucleus is at (Z, N) = (6, 8), which corresponds to Carbon-14 (14^C). The final nucleus is at (Z, N) = (7, 7), which corresponds to Nitrogen-14 (14^N).
2. Recognize that the red arrow indicates a beta decay process, where a neutron is converted into a proton, emitting a beta particle (electron) and an antineutrino.
3. Write the general form of the beta decay equation: ^A_ZX -> ^A_{Z+1}Y + ^0_{-1}e + antineutrino.
4. Substitute the identified nuclei into the equation: ^14_6C -> ^14_7N + ^0_{-1}e + antineutrino.
5. Ensure the equation is balanced in terms of both mass number (A) and atomic number (Z). The mass number remains 14 on both sides, and the atomic number increases from 6 to 7, with the emission of a beta particle (electron) balancing the charge.

Key Concepts

Beta Decay

Beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted from an atomic nucleus. This process occurs when a neutron in the nucleus transforms into a proton, emitting an electron (beta-minus decay) or when a proton transforms into a neutron, emitting a positron (beta-plus decay). Understanding beta decay is crucial for writing balanced nuclear equations.

Nuclear Equation

A nuclear equation represents the transformation of atomic nuclei during radioactive decay or nuclear reactions. It includes the symbols for the reactants and products, along with their atomic numbers and mass numbers. Balancing nuclear equations is essential to ensure that the number of nucleons (protons and neutrons) and charge are conserved during the reaction.

Conservation of Mass and Charge

In nuclear reactions, the conservation of mass and charge states that the total mass number and total charge must remain constant before and after the reaction. This principle is fundamental when balancing nuclear equations, as it ensures that the number of protons and neutrons, as well as the overall charge, are equal on both sides of the equation.