Natural gold has only one stable isotope, ^19779 gold is...

Natural gold has only one stable isotope, $^{197}_{79}$ gold is bombarded with slow neutrons, $\beta^{-}$ particles are emitted.
a. Write the appropriate reaction equation.
b. Calculate the maximum energy of the emitted beta particles

Key Concepts

Nuclear Reaction Equations

This concept involves writing balanced representations of nuclear processes where the sum of the mass numbers (total nucleons) and the atomic numbers (total protons) are conserved in a reaction. It is essential for translating a descriptive nuclear process into a formal reaction equation, indicating the transformation of elements as neutrons interact with nuclei and decay occurs.

Beta Decay

Beta decay is a type of radioactive decay in which a neutron in a nucleus is converted into a proton, resulting in the emission of an electron (called a beta particle) and an antineutrino. This process increases the atomic number of the nucleus by one while keeping the mass number constant, and it features a characteristic continuous energy spectrum for the emitted beta particle, whose maximum energy is determined by the Q-value of the decay.

Q-value and Energy Calculations in Nuclear Decay

The Q-value of a nuclear reaction or decay represents the net energy released and is based on the mass difference between the initial and final states converted to energy using Einstein’s equation (E = ?m·c²). This value is critical for calculating the maximum kinetic energy available to decay products such as beta particles, and for understanding the energetics of nuclear transformations.

Neutron Activation

Neutron activation refers to the process where stable nuclei capture neutrons, becoming heavier and often unstable isotopes. This technique is commonly used to produce radioactive isotopes which may subsequently undergo decay, such as beta emission, and is pivotal in various applications from medical isotope production to materials analysis.