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Ch.2 - Atoms, Molecules, and Ions
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBrown 14th EditionCh.2 - Atoms, Molecules, and IonsProblema 90c1
Capitolo 2, Problema 90c1

"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:
Comparison of two atomic arrangements: (i) square grid and (ii) close-packed arrangement.
(c) By what factor has the number of atoms on the surface increased in going to arrangement B from arrangement A?

Guida verificata passo dopo passo
1
Determine the area occupied by a single atom in arrangement A (square grid). The area of a square is given by the side length squared. Here, the side length is the diameter of the atom.
Calculate the area occupied by a single atom in arrangement B (close-packed arrangement). In this arrangement, each atom is surrounded by six others, forming a hexagon. The area of a hexagon can be calculated using the formula: \( \frac{3\sqrt{3}}{2} \times (\text{radius})^2 \).
Compare the areas calculated in steps 1 and 2 to determine the relative packing densities of the two arrangements.
Calculate the number of atoms per unit area for both arrangements by taking the reciprocal of the area occupied by a single atom in each arrangement.
Determine the factor by which the number of atoms on the surface has increased by dividing the number of atoms per unit area in arrangement B by the number of atoms per unit area in arrangement A.

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Atomic Arrangement

Atomic arrangement refers to the spatial organization of atoms in a material. In the context of the question, arrangement A depicts a square grid where atoms are aligned in rows and columns, while arrangement B shows a close-packed structure where atoms occupy the depressions of the previous row, maximizing density and minimizing empty space.
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Atom Structure

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. This arrangement is more efficient than a simple grid because it allows for more atoms to fit into the same area, leading to a higher atomic density and potentially greater material strength.
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Crystalline Solids Structure

Surface Density

Surface density is a measure of how many atoms are present per unit area on a surface. In comparing arrangements A and B, calculating the surface density will reveal how many more atoms can be accommodated in the close-packed arrangement compared to the square grid, thus allowing for the determination of the factor by which the number of atoms has increased.
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Density Concepts
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Domanda del libro di testo

A cube of gold that is 1.00 cm on a side has a mass of 19.3 g. A single gold atom has a mass of 197.0 u. (b) From the information given, estimate the diameter in Å of a single gold atom.

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Domanda del libro di testo

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?

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Domanda del libro di testo

"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?"

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Domanda del libro di testo

(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?

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Domanda del libro di testo

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

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Domanda del libro di testo
Very small semiconductor crystals, composed of approximately 1000 to 10,000 atoms, are called quantum dots. Quantum dots made of the semiconductor CdSe are now being used in electronic reader and tablet displays because they emit light efficiently and in multiple colors, depending on dot size. The density of CdSe is 5.82 g/cm3. (b) CdSe quantum dots that are 2.5 nm in diameter emit blue light upon stimulation. Assuming that the dot is a perfect sphere and that the empty space in the dot can be neglected, calculate how many Cd atoms are in one quantum dot of this size.
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