The radioactive isotope 100Tc decays to form the stable iso-tope 100Mo. (a) There are two possible pathways for this decay. Write balanced equations for both.

Verified step by step guidance

1. Identify the atomic numbers of the isotopes involved. Technetium (Tc) has an atomic number of 43, and Molybdenum (Mo) has an atomic number of 42.
2. Recognize that the decay of 100Tc to 100Mo involves a change in the atomic number, indicating the involvement of either beta decay or electron capture.
3. Write the equation for beta decay. In beta decay, a neutron in the nucleus of 100Tc is converted into a proton, and a beta particle (electron) is emitted. The atomic number increases by 1. However, since the atomic number must decrease from 43 to 42, beta decay is not a suitable pathway.
4. Write the equation for electron capture. In electron capture, an electron from the inner shell is captured by the nucleus, where it combines with a proton to form a neutron, decreasing the atomic number by 1. The equation is: \( ^{100}_{43}Tc + e^- \rightarrow ^{100}_{42}Mo + \nu_e \), where \( e^- \) is the captured electron and \( \nu_e \) is the neutrino emitted.
5. Consider the possibility of positron emission, another pathway that decreases the atomic number by 1. In positron emission, a proton in the nucleus is converted into a neutron, and a positron is emitted. The equation is: \( ^{100}_{43}Tc \rightarrow ^{100}_{42}Mo + e^+ \), where \( e^+ \) is the positron.

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur through various pathways, including alpha decay, beta decay, and gamma decay. Each pathway results in the transformation of the original isotope into a different element or isotope, often leading to a more stable configuration.

Balanced Chemical Equations

A balanced chemical equation represents a chemical reaction where the number of atoms for each element is the same on both sides of the equation. This is crucial for obeying the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Balancing equations involves adjusting coefficients to ensure that the total number of each type of atom is equal.

Isotopes

Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For example, 100Tc and 100Mo are isotopes of technetium and molybdenum, respectively. Understanding isotopes is essential in nuclear chemistry, especially in processes like radioactive decay, where one isotope transforms into another.