Ch.7 - Periodic Properties of the Elements

Problem 21a

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Chapter 7, Problem 21a

Tungsten has the highest melting point of any metal in the periodic table: 3422°C. The distance between the centers of W atoms in tungsten metal is 2.74 Å. a. What is the atomic radius of a tungsten atom in this environment? (This radius is called the metallic radius.)

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Understand that in a metallic crystal, atoms are arranged in a lattice structure where each atom is surrounded by others, and the distance given is between the centers of two adjacent atoms.

Recognize that the metallic radius is defined as half the distance between the nuclei of two adjacent atoms in a metal lattice.

Use the given distance between the centers of tungsten atoms, which is 2.74 Å, to find the metallic radius.

Calculate the metallic radius by dividing the given distance by 2, since the metallic radius is half of this distance.

Express the metallic radius in the same units as the given distance, which is Ångströms (Å).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Metallic Radius

The metallic radius is defined as half the distance between the centers of two adjacent metal atoms in a metallic lattice. It reflects the size of the atom in a metallic state, where atoms are closely packed. In the case of tungsten, the metallic radius can be calculated by taking half of the interatomic distance provided, which is essential for understanding the spatial arrangement of atoms in metals.

Interatomic Distance

Interatomic distance refers to the distance between the nuclei of two adjacent atoms in a solid. This measurement is crucial in determining the structure and properties of materials, particularly in metals where atoms are closely packed. For tungsten, the given interatomic distance of 2.74 Å allows us to derive the metallic radius, highlighting the compact nature of metallic bonding.

Periodic Trends

Periodic trends refer to the predictable patterns observed in the properties of elements as one moves across or down the periodic table. These trends include atomic radius, ionization energy, and electronegativity. Understanding these trends helps in predicting the behavior of elements, such as tungsten, and their interactions based on their position in the periodic table, which is relevant when discussing properties like melting point and atomic size.

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Periodic Trends

Related Practice

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the 𝑛=3 electron shell: K, Mg, P, Rh, Ti.

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Textbook Question

With the exception of helium, the noble gases condense to form solids when they are cooled sufficiently. At temperatures below 83 K, argon forms a close-packed solid whose structure is shown below. (b) Is this value larger or smaller than the bonding atomic radius estimated for argon in Figure 7.7?

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Textbook Question

With the exception of helium, the noble gases condense to form solids when they are cooled sufficiently. At temperatures below 83 K, argon forms a close-packed solid whose structure is shown below. (c) Based on this comparison would you say that the atoms are held together by chemical bonds in solid argon?

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Textbook Question

Tungsten has the highest melting point of any metal in the periodic table: 3422°C. The distance between the centers of W atoms in tungsten metal is 2.74 Å. c. If you put tungsten metal under high pressure, predict what would happen to the distance between W atoms.

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Textbook Question

Which of the following statements about the bonding atomic radii in Figure 7.7 is incorrect? (i) For a given period, the radii of the representative elements generally decrease from left to right across a period. (ii) The radii of the representative elements for the n = 3 period are all larger than those of the corresponding elements in the n = 2 period. (iii) For most of the representative elements, the change in radius from the n = 2 to the n = 3 period is greater than the change in radius from n = 3 to n = 4. (iv) The radii of the transition elements generally increase moving from left to right within a period. (v) The large radii of the Group 1 elements are due to their relatively small effective nuclear charges.

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Textbook Question

Estimate the As¬I bond length from the data in Figure 7.7 and compare your value to the experimental As ¬I bond length in arsenic triiodide, AsI₃, 2.55 Å.

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