Arrange the following metals in increasing order of expected melting point: La, W, Ta, Hf. Explain this trend in melting points.

First, let's understand the factors that affect the melting points of elements. Melting point is the temperature at which a solid changes into a liquid. The key factors that affect the melting points are: 1. Atomic size: Larger atoms have weaker metallic bonds which result in lower melting points. 2. Crystal lattice structure: Different metals have different crystal lattice structures, which affect the strength of their metallic bonds and, consequently, their melting points. 3. Number of valence electrons: Metals with more valence electrons tend to form stronger metallic bonds, resulting in higher melting points. 4. Electronegativity: Higher electronegativity values indicate stronger attractive forces between atoms, leading to higher melting points. Now that we understand the factors affecting melting points, let's analyze La, W, Ta, and Hf using these factors.

La (Lanthanum): La is a large atom and its atomic size is the largest among the given metals. It has 3 valence electrons and a relatively low electronegativity. W (Tungsten): W is a smaller atom than La. It has 6 valence electrons and belongs to the d-block of the periodic table. It has a high electronegativity value. Ta (Tantalum): Ta is very similar to W in size, electronegativity, and number of valence electrons (5). Both W and Ta belong to Group 5 and have very similar properties. Ta also has a high electronegativity value. Hf (Hafnium): Hf has a similar size to Ta and W, but less valence electrons (4) and a slightly lower electronegativity value.

Taking into account the factors of atomic size, crystal lattice structure, number of valence electrons, and electronegativity, we can arrange the metals in increasing order of their expected melting points as follows: La < Hf < Ta < W That is, Lanthanum (La) has the lowest expected melting point and Tungsten (W) has the highest expected melting point.

We can explain the trend observed in the melting points of La, W, Ta, and Hf using the factors analyzed in Steps 1 and 2: La has a larger atomic size than the other metals, which leads to weaker metallic bonds and a lower melting point. Additionally, it has fewer valence electrons and a lower electronegativity value, which also contribute to its lower melting point. Hf has a similar atomic size to Ta and W but has fewer valence electrons and a slightly lower electronegativity value, resulting in a higher melting point than La but lower than Ta and W. Ta has a smaller atomic size than La and Hf, and also has more valence electrons than both of them, which leads to a higher melting point. Moreover, it has a high electronegativity value, contributing to its high melting point. W has the smallest atomic size and the highest electronegativity value among the given metals, which results in stronger metallic bonds and the highest melting point. It also has more valence electrons than La and Hf, further contributing to its higher melting point.