Write balanced nuclear equations for the following transformations: (d) gold-188 decays by positron emission.

Verified step by step guidance

1. Identify the initial isotope involved in the decay process. In this case, it is gold-188, which is represented as \( ^{188}_{79}\text{Au} \).
2. Understand the type of decay occurring. Positron emission involves the conversion of a proton into a neutron, releasing a positron (\( \beta^+ \)) and a neutrino.
3. Write the general form of the nuclear equation for positron emission: \( ^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + \beta^+ \). Here, \( A \) is the mass number, \( Z \) is the atomic number, \( X \) is the parent nucleus, and \( Y \) is the daughter nucleus.
4. Apply the general form to the specific case of gold-188: \( ^{188}_{79}\text{Au} \rightarrow ^{188}_{78}\text{Pt} + \beta^+ \). Note that the atomic number decreases by one, while the mass number remains the same.
5. Verify that the equation is balanced by checking that the sum of atomic numbers and mass numbers are equal on both sides of the equation. This ensures the conservation of charge and mass in the nuclear reaction.