Atomic Radius of Gold

Questions and Answers

What is the type of crystal structure gold adopts in its solid form?

Hexagonal close-packed

Body-centered cubic

Face-centered cubic (correct)

Simple cubic

Which of the following is used to calculate the atomic radius of gold?

n = 1

Bragg equation (correct)

Density of gold

All of the above

How many atoms are there effectively in one unit cell of a face-centered cubic structure?

4 (correct)

The distance (in picometers) between crystal layers can be determined using which equation?

$BC + CD = 2d \sin\theta$ Signup and view all the answers

What is the density of gold, which is necessary for calculating its atomic radius?

19.3 g/cm³ Signup and view all the answers

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?

14.170 degrees Signup and view all the answers

What is the coordination number for both hexagonal close-packed and cubic close-packed structures?

12 Signup and view all the answers

How many atoms are contained in a body-centered cubic unit cell?

2 Signup and view all the answers

Which of the following arrangements represents a face-centered cubic structure?

ABCABCABCABC… layering Signup and view all the answers

What is the relationship between atomic radius and edge length in the cubic close-packed structure?

Edge length = 2 x atomic radius Signup and view all the answers

What is the most stable form of solid magnesium (Mg)?

Hexagonal close-packed Signup and view all the answers

Which type of crystal structure is characterized by having 4 atoms per unit cell?

Face-centered cubic Signup and view all the answers

In a hexagonal close-packed structure, how are the layers arranged?

ABABAB layering Signup and view all the answers

What is the density of gold (Au) which crystallizes in a cubic close-packed structure?

19.3 g/cm3 Signup and view all the answers

Which unit cell type has the highest coordination number?

Face-centered cubic cell Signup and view all the answers

What is a characteristic feature of crystalline solids compared to amorphous solids?

Crystalline solids have a uniform arrangement of particles. Signup and view all the answers

How many particles are present in one unit cell of a body-centered cubic (bcc) structure?

2 Signup and view all the answers

Which type of packing leads to the maximum space efficiency in a crystalline solid?

Face-centered cubic packing Signup and view all the answers

What defines the 'unit cell' of a crystalline structure?

The basic repeating structural unit in a crystalline solid. Signup and view all the answers

Identify the correct statement about hydrogen bonds.

They involve a hydrogen atom bonded to N, O, or F. Signup and view all the answers

Which of the following properties is true for amorphous solids?

They have a wide range of melting points. Signup and view all the answers

What factor increases the polarizability of an atom or molecule?

Greater number of electrons Signup and view all the answers

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!