The first six elements of the first transition series have the following number of stable isotopes:
Element Number of Stable Isotopes
Sc 1
Ti 5
V 1
Cr 3
Mn 1
Fe 4
Explain why Sc, V, and Mn each have only one stable isotope while the other elements have several.

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons. The stability of an isotope is determined by the balance between the nuclear forces that hold the nucleus together and the repulsive forces between protons. Stable isotopes do not undergo radioactive decay, while unstable isotopes do. The stability of isotopes can vary significantly among elements, influencing the number of stable isotopes an element possesses.

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is a measure of the stability of a nucleus; higher binding energy generally indicates a more stable nucleus. The ratio of neutrons to protons plays a crucial role in determining binding energy, as certain ratios lead to more stable configurations. Elements with a favorable neutron-to-proton ratio tend to have multiple stable isotopes, while those with less favorable ratios may have only one.

Magic numbers refer to specific numbers of protons or neutrons in a nucleus that result in a more stable configuration due to complete energy levels. For example, nuclei with magic numbers of protons or neutrons exhibit greater stability and are less likely to undergo decay. The first transition series elements exhibit varying stability based on their neutron and proton counts relative to these magic numbers, explaining why some elements like Sc, V, and Mn have only one stable isotope while others have multiple.