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Chapter 12: Problem 48

How do you account for the observation that the alkali metals, like sodium and potassium, are soft enough to be cut with a knife?

Short Answer

Expert verified
The softness of alkali metals, like sodium and potassium, can be attributed to their electron configuration with only one valence electron, which leads to weak metallic bonding. Additionally, their large atomic radii result in a low atomic packing factor and weaker inter-atomic forces in the lattice structure, further contributing to their softness.

Step by step solution

01

Understand Alkali Metals Properties

Alkali metals, including sodium and potassium, are found in Group 1 of the periodic table. These elements have one electron in their outermost energy level, making them highly reactive. They are also soft, with low melting and boiling points. The softness of alkali metals is attributed to their metallic bonding and electron configuration.
02

Electron Configuration

Alkali metals have one electron in the outermost electron shell or energy level. This outer electron experiences a weak attraction to the nucleus, which consists of protons and neutrons. The electron is shielded from the positive charge of the nucleus by the inner electron shells. In sodium (Na), the electron configuration is \(1s^2 2s^2 2p^6 3s^1\), and in potassium (K), it is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\). The single outer electron in each case is responsible for their high reactivity and other properties.
03

Metallic Bonding

In metallic bonding, free electrons move through a lattice of positively charged metal ions. The strength of metallic bonding depends on the number of electrons available for bonding and the effective nuclear charge. Alkali metals have only one valence electron, which contributes to weaker metallic bonding, leading to lower hardness and higher softness in these elements.
04

Low Atomic Packing Factor

The atomic packing factor (APF) is a measure of how closely packed the atoms are in a crystal structure. In alkali metals, the atoms have a relatively low atomic packing factor due to their large atomic radii. Sodium and potassium have body-centered cubic (BCC) crystal structures that lead to lower packing efficiency. This results in weaker inter-atomic forces in the metal lattice, contributing to their softness. In summary, the softness of alkali metals like sodium and potassium can be attributed to their weak metallic bonding due to having only one valence electron, their large atomic radii leading to a low atomic packing factor, and weaker inter-atomic forces in the lattice structure.

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Most popular questions from this chapter

Covalent bonding occurs in both molecular and covalent network solids. Why do these two kinds of solids differ so greatly in their hardness and melting points?

Of the seven three-dimensional primitive lattices, which ones have a unit cell where no two lattice vectors are perpendicular to each other?

Cadmium telluride, CdTe, takes the zinc blende structure (Figure 12.26 ) with a unit cell edge length of \(6.49 \AA\). There are four cadmium atoms and four tellurium atoms per unit cell. How many of each type of atom are there in a cubic crystal with an edge length of \(5.00 \mathrm{nm} ?\)

For each of the following alloy compositions indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound: (a) \(\mathrm{Cu}_{0.66} \mathrm{Zn}_{0.34},\) (b) \(\mathrm{Ag}_{3} \mathrm{Sn}\) (c) \(\mathrm{Ti}_{0.99} \mathrm{O}_{0.01}\)

In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation \((\lambda),\) the angle at which the radiation is diffracted \((\theta),\) and the distance between planes of atoms in the crystal that cause the diffraction \((d)\) is given by \(n \lambda=2 d \sin \theta .\) X-rays from a copper X-ray tube that have a wavelength of \(1.54 \AA\) are diffracted at an angle of 14.22 degrees by crystalline silicon. Using the Bragg equation, calculate the distance between the planes of atoms responsible for diffraction in this crystal, assuming \(n=1\) (first-order diffraction).
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