Ch.2 - Atoms, Molecules, and Ions

Problem 90c2

Chapter 2, Problem 90c2

"The diameter of a rubidium atom is 495 pm We will consider two different ways of placing the atoms on a surface. In arrangement A, all the atoms are lined up with one another to form a square grid. Arrangement B is called a close-packed arrangement because the atoms sit in the 'depressions' formed by the previous row of atoms:

(c) If extended to three dimensions, which arrangement would lead to a greater density for Rb metal?"

Verified step by step guidance

Identify the two arrangements: (i) square grid and (ii) close-packed arrangement.

Understand that density is defined as mass per unit volume.

In a square grid (i), atoms are aligned in rows and columns, leading to more empty space between atoms.

In a close-packed arrangement (ii), atoms are positioned in the 'depressions' of the previous row, reducing empty space and increasing packing efficiency.

Conclude that the close-packed arrangement (ii) would lead to a greater density for Rb metal when extended to three dimensions, as it minimizes empty space and maximizes the number of atoms per unit volume.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

15m

Was this helpful?

Key Concepts

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

Atomic Arrangement

Atomic arrangement refers to the spatial organization of atoms in a material. In the context of the question, arrangement A is a square grid where atoms are aligned in a flat, two-dimensional pattern, while arrangement B is a close-packed structure where atoms occupy the depressions of the previous layer, maximizing the use of space. Understanding these arrangements is crucial for analyzing how they affect the density of the material.

Density

Density is defined as mass per unit volume and is a key property of materials. In the context of atomic arrangements, a higher density indicates that more atoms are packed into a given volume. The question asks which arrangement leads to greater density, which can be determined by considering how closely the atoms are packed in three dimensions.

Close-Packing

Close-packing is a method of arranging spheres (or atoms) in a way that maximizes the number of spheres in a given volume. In three dimensions, close-packed arrangements, such as face-centered cubic (FCC) or hexagonal close-packed (HCP), allow for more efficient use of space compared to simple arrangements like a square grid. This concept is essential for understanding why arrangement B would lead to a greater density for rubidium metal.

Recommended video:

Guided course

01:31

Crystalline Solids Structure

Related Practice

Textbook Question

The diameter of a rubidium atom is 495 pm We will consider two different ways of placing the atoms on a surface. In arrangement A, all the atoms are lined up with one another to form a square grid. Arrangement B is called a close-packed arrangement because the atoms sit in the 'depressions' formed by the previous row of atoms: (a) Using arrangement A, how many Rb atoms could be placed on a square surface that is 1.0 cm on a side?

views

Textbook Question

(b) How many molecules of C13H18O2 are in this tablet?

Textbook Question

"The diameter of a rubidium atom is 495 pm We will consider two different ways of placing the atoms on a surface. In arrangement A, all the atoms are lined up with one another to form a square grid. Arrangement B is called a close-packed arrangement because the atoms sit in the 'depressions' formed by the previous row of atoms:

Textbook Question

Very small semiconductor crystals, composed of approximately1000 to 10,000 atoms, are called quantum dots.Quantum dots made of the semiconductor CdSe are nowbeing used in electronic reader and tablet displays becausethey emit light efficiently and in multiple colors, dependingon dot size. The density of CdSe is 5.82 g/cm3.(b) CdSe quantum dots that are 2.5 nm in diameter emitblue light upon stimulation. Assuming that the dot is aperfect sphere and that the empty space in the dot canbe neglected, calculate how many Cd atoms are in onequantum dot of this size.

Textbook Question

(a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus?

views

Textbook Question

(b) Using the mass of the proton from Table 2.1 and assuming its diameter is 1.0 * 10-15 m, calculate the density of a proton in g>cm3.

views