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Questions and Answers
What is the type of crystal structure gold adopts in its solid form?
What is the type of crystal structure gold adopts in its solid form?
Which of the following is used to calculate the atomic radius of gold?
Which of the following is used to calculate the atomic radius of gold?
How many atoms are there effectively in one unit cell of a face-centered cubic structure?
How many atoms are there effectively in one unit cell of a face-centered cubic structure?
The distance (in picometers) between crystal layers can be determined using which equation?
The distance (in picometers) between crystal layers can be determined using which equation?
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What is the density of gold, which is necessary for calculating its atomic radius?
What is the density of gold, which is necessary for calculating its atomic radius?
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If X-rays of wavelength 0.154 nm are used, at what angle were they diffracted to determine the distance between layers in the crystal?
If X-rays of wavelength 0.154 nm are used, at what angle were they diffracted to determine the distance between layers in the crystal?
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What is the coordination number for both hexagonal close-packed and cubic close-packed structures?
What is the coordination number for both hexagonal close-packed and cubic close-packed structures?
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How many atoms are contained in a body-centered cubic unit cell?
How many atoms are contained in a body-centered cubic unit cell?
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Which of the following arrangements represents a face-centered cubic structure?
Which of the following arrangements represents a face-centered cubic structure?
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What is the relationship between atomic radius and edge length in the cubic close-packed structure?
What is the relationship between atomic radius and edge length in the cubic close-packed structure?
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What is the most stable form of solid magnesium (Mg)?
What is the most stable form of solid magnesium (Mg)?
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Which type of crystal structure is characterized by having 4 atoms per unit cell?
Which type of crystal structure is characterized by having 4 atoms per unit cell?
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In a hexagonal close-packed structure, how are the layers arranged?
In a hexagonal close-packed structure, how are the layers arranged?
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What is the density of gold (Au) which crystallizes in a cubic close-packed structure?
What is the density of gold (Au) which crystallizes in a cubic close-packed structure?
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Which unit cell type has the highest coordination number?
Which unit cell type has the highest coordination number?
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What is a characteristic feature of crystalline solids compared to amorphous solids?
What is a characteristic feature of crystalline solids compared to amorphous solids?
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How many particles are present in one unit cell of a body-centered cubic (bcc) structure?
How many particles are present in one unit cell of a body-centered cubic (bcc) structure?
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Which type of packing leads to the maximum space efficiency in a crystalline solid?
Which type of packing leads to the maximum space efficiency in a crystalline solid?
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What defines the 'unit cell' of a crystalline structure?
What defines the 'unit cell' of a crystalline structure?
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Identify the correct statement about hydrogen bonds.
Identify the correct statement about hydrogen bonds.
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Which of the following properties is true for amorphous solids?
Which of the following properties is true for amorphous solids?
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What factor increases the polarizability of an atom or molecule?
What factor increases the polarizability of an atom or molecule?
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Study Notes
Atomic Radius Calculation of Gold
- Gold (Au) has an atomic mass of 197.0 g/mol and a density of 19.3 g/cm³.
- Gold crystallizes in a face-centered cubic (fcc) structure, with 4 atoms per unit cell.
- Each fcc unit cell features 1/8 of an atom at each of the 8 corners and 1/2 of an atom on each of the 6 faces.
- Volume of the unit cell (V) can be calculated using the formula: V = a³, where 'a' is the edge length.
X-ray Diffraction
- X-ray diffraction involves the scattering of X-rays by the crystalline structure of solids.
- A diffraction pattern results from the interference of X-ray waves scattered by electron clouds of atoms.
- Bragg's Law is represented as BC + CD = 2d sinθ = nλ, relating angle θ, wavelength λ, and spacing d between crystal layers.
Closest Packing Structures
- Closest packing involves efficient arrangement of spheres, minimizing empty space.
- Two main types: Hexagonal close-packed (hcp) and Cubic close-packed (ccp), featuring different layering (ABAB... vs. ABC...).
- For hcp, each unit cell has 6 particles; for ccp, each unit cell has 4 particles.
- Coordination number for both structures is 12, indicating contact between each atom and 12 adjacent atoms.
Intermolecular Forces
- Dispersion forces increase with the number of electrons and electron cloud diffuseness.
- Hydrogen bonds are special dipole-dipole interactions occurring between hydrogen atoms in polar bonds and highly electronegative atoms (N, O, F).
Crystalline vs. Amorphous Solids
- Crystalline solids have a uniform atomic arrangement and sharp melting points, making them anisotropic.
- Amorphous solids have a random atomic arrangement and a wide melting point range, making them isotropic.
Unit Cells and Packing
- A unit cell is the fundamental repeating unit in a crystal structure, represented by lattice points.
- Types of unit cells:
- Simple Cubic (scc): 1 atom/unit cell, 52% space occupied, coordination number = 6.
- Body-Centered Cubic (bcc): 2 atoms/unit cell, 68% space occupied, coordination number = 8.
- Face-Centered Cubic (fcc): 4 atoms/unit cell, 74% space occupied, coordination number = 12.
- Each unit cell shares its atoms with neighboring cells, maximizing structural efficiency.
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Description
This quiz focuses on calculating the atomic radius of gold using its crystallization in a cubic close-packed structure. Through understanding the volume of the unit cell and the distribution of atoms, you'll gain insight into atomic properties. Dive into the fascinating world of atomic structure and measurements!