The melting points for the second-series transition elements increase from 1522 °C for yttrium to 2623 °C for molybdenum and then decrease to 321 °C for cadmium. Account for the trend using band theory.

Verified step by step guidance

1. Understand the basic concept of band theory, which explains that in metals, the valence and conduction bands overlap, allowing electrons to flow freely. This electron mobility contributes to the metallic properties such as conductivity and malleability.
2. Recognize that the melting point of a metal is influenced by the strength of the metallic bonds, which in turn depends on the electron density in the 'sea' of delocalized electrons. More delocalized electrons generally mean stronger metallic bonds and higher melting points.
3. Consider the electron configuration of the transition metals. As you move from yttrium to molybdenum in the periodic table, the number of electrons in the d-orbital increases. This increase in d-electrons enhances the metallic bonding by providing more electrons that can delocalize and participate in bonding.
4. Note the decrease in melting point after molybdenum. This can be attributed to the filling of the d-orbitals and the beginning of the filling of the next s-orbital, which can lead to a decrease in bonding strength. The filled d-orbitals do not contribute as effectively to metallic bonding compared to partially filled d-orbitals.
5. Relate the changes in the electronic structure to the observed trend in melting points. The increase in melting points from yttrium to molybdenum corresponds to an increase in the number of delocalized d-electrons, enhancing metallic bonding. The subsequent decrease after molybdenum is due to the completion of the d-orbital and reduced effectiveness in metallic bonding.

Key Concepts

Band Theory

Band theory explains the electronic structure of solids, particularly metals and semiconductors, by describing how atomic orbitals combine to form energy bands. In transition metals, the presence of partially filled d-orbitals allows for the formation of conduction bands, which influence electrical and thermal properties, including melting points.

Transition Metals and d-Orbitals

Transition metals are characterized by their d-orbitals, which can accommodate varying numbers of electrons. The filling of these d-orbitals affects the metallic bonding strength and, consequently, the melting points. As the d-orbitals fill, the increased electron-electron interactions can lead to stronger metallic bonds, resulting in higher melting points.

Melting Point Trends in Transition Metals

The melting points of transition metals exhibit a unique trend due to the interplay of metallic bonding and crystal structure. Initially, melting points increase due to stronger bonding from filled d-orbitals, peaking at elements like molybdenum. However, as the d-orbitals become more filled and the structure changes, the melting points can decrease, as seen in cadmium, where weaker bonding leads to lower melting temperatures.