Skip to main content
Ch.12 - Solids and Modern Materials
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBrown 15th EditionCh.12 - Solids and Modern MaterialsProblema 36a
Capitolo 12, Problema 36a

Calcium crystallizes in a body-centered cubic structure at 467°C. (a) How many Ca atoms are contained in each unit cell?

Guida verificata passo dopo passo
1
Understand the structure: A body-centered cubic (BCC) structure has atoms at each corner of the cube and one atom in the center of the cube.
Calculate the contribution of corner atoms: Each corner atom is shared by 8 adjacent unit cells, so each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
Calculate the total contribution from corner atoms: Since there are 8 corners in a cube, the total contribution from corner atoms is \( 8 \times \frac{1}{8} = 1 \) atom.
Consider the center atom: In a BCC structure, there is one whole atom located at the center of the cube, contributing fully to the unit cell.
Add the contributions: The total number of Ca atoms in a BCC unit cell is the sum of the corner atoms and the center atom, which is \( 1 + 1 = 2 \) atoms.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Body-Centered Cubic (BCC) Structure

The body-centered cubic (BCC) structure is a type of crystal lattice where atoms are located at each of the eight corners of a cube and a single atom is positioned at the center of the cube. This arrangement results in a coordination number of 8, meaning each atom is in contact with eight neighboring atoms. Understanding this structure is essential for determining the number of atoms per unit cell.
Video consigliato:
Percorso guidato
00:40
Body Centered Cubic Example

Unit Cell

A unit cell is the smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal. It defines the arrangement of atoms in the crystal and is characterized by its dimensions and angles. In the case of BCC, the unit cell contains a specific number of atoms that can be calculated based on the arrangement of atoms within the cell.
Video consigliato:
Percorso guidato
01:27
Simple Cubic Unit Cell

Atomic Packing Factor (APF)

The atomic packing factor (APF) is a measure of how efficiently atoms are packed in a unit cell. It is calculated as the ratio of the volume occupied by the atoms in the unit cell to the total volume of the unit cell. For BCC structures, the APF is approximately 0.68, indicating that 68% of the volume is filled with atoms, which helps in understanding the density and stability of the crystal structure.
Video consigliato:
Percorso guidato
01:56
Conversion Factors
Pratica correlata
Domanda del libro di testo

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (b) Which structure(s) corresponds to the least dense packing of atoms?

454
views
Domanda del libro di testo

Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3. (a) Use this information and Avogadro’s number (NA = 6.022 × 1023/mol) to estimate the atomic radius of sodium. (b) If sodium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close-packed metal. Would it still float on water?

1701
views
1
comments
Domanda del libro di testo

Calcium crystallizes in a face-centered cubic unit cell at room temperature that has an edge length of 5.588 Å.

a. Calculate the atomic radius of a calcium atom.

b. Calculate the density of Ca metal at this temperature.