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Chapter 7: Problem 19

Tungsten has the highest melting point of any metal in the periodic table: \(3422{ }^{\circ} \mathrm{C}\). The distance between \(\mathrm{W}\) atoms in tungsten metal is \(2.74 \AA\). (a) What is the atomic radius of a tungsten atom in this environment? (This radius is called the metallic radius.) (b) If you put tungsten metal under high pressure, predict what would happen to the distance between \(\mathrm{W}\) atoms.

Short Answer

Expert verified
The atomic (metallic) radius of a tungsten atom is approximately \(1.37 \AA\). Under high pressure, the distance between tungsten atoms is expected to decrease as the atoms are forced to move closer together.

Step by step solution

01

Understanding the relationship between atomic radius and distance between atoms

In a metallic crystal, the distance between two adjacent atoms gives an approximate estimation of their combined atomic radii. As the atoms are closely packed, we can assume that the distance between the centers of two tungsten atoms is approximately equal to the sum of their atomic radii. So, we can represent that as follows: Distance between atoms = 2 * Atomic radius of tungsten
02

Calculate the atomic radius of tungsten

Given that the distance between tungsten atoms is 2.74 Å (Angstrom), we can use the above equation to calculate the atomic radius of tungsten: \(2 * Atomic\, radius\, of\, tungsten = 2.74 \AA\) Divide both sides by 2 to find the atomic radius of tungsten: \(Atomic\, radius\, of\, tungsten = 1.37 \AA\) So, the atomic (metallic) radius of a tungsten atom is approximately 1.37 Å.
03

Predict the effect of high pressure on the distance between tungsten atoms

Under high pressure, atoms are forced to move closer together. Since the metallic crystal is closely packed, we can predict that the distance between tungsten atoms will decrease under high pressure. The atomic radii themselves are not expected to change significantly, but the increased pressure will cause the atoms to be more tightly packed. In conclusion, the atomic radius of a tungsten atom in its metallic environment is approximately 1.37 Å, and the distance between tungsten atoms is expected to decrease under high pressure.

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Most popular questions from this chapter

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Potassium metal burns in an atmosphere of chlorine gas. (b) Strontium oxide is added to water. (c) A fresh surface of lithium metal is exposed to oxygen gas. (d) Sodium metal is reacted with molten sulfur.

What is the relationship between the ionization energy of an anion with a 1 - charge such as \(\mathrm{F}^{-}\) and the electron affinity of the neutral atom, F?

Note from the following table that the increase in atomic radius in moving from \(\mathrm{Zr}\) to \(\mathrm{Hf}\) is smaller than in moving from \(\mathrm{Y}\) to La. Suggest an explanation for this effect. \begin{tabular}{llll} \hline \multicolumn{3}{l} { Atomic Radii \((\AA)\)} \\ \hline Sc & 1.44 & \(\mathrm{Ti}\) & 1.36 \\ \(\mathrm{Y}\) & 1.62 & \(\mathrm{Zr}\) & 1.48 \\ \(\mathrm{La}\) & 1.69 & \(\mathrm{Hf}\) & 1.50 \end{tabular}

Write electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cr}^{3+}\), (b) \(\mathrm{N}^{3-},(\mathrm{c}) \mathrm{Sc}^{3+},(\mathrm{d}) \mathrm{Cu}^{2+}\) (e) \(\mathrm{Tl}^{+}\), (f) \(\mathrm{Au}^{+}\).

Use electron configurations to explain the following observations: (a) The first ionization energy of phosphorus is greater than that of sulfur. (b) The electron affinity of nitrogen is lower (less negative) than those of both carbon and oxygen. (c) The second ionization energy of oxygen is greater than the first ionization energy of fluorine. (d) The third ionization energy of manganese is greater than those of both chromium and iron.
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