QUESTION What is the mass (in kg) of a 1 cubic foot block of Copper? (units are intentionally in both systems) Approach and tasks 1. We will watch the following video to understand how to calculate density of an element using the periodic table and knowledge about the structure of the element. Calculating mass from atomic information: https://www.youtube.com/watch?v=odcZBJ_eQrE 2. You will develop a pseudo-code for

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What is the mass (in kg) of a 1 cubic foot block of Copper? (units are intentionally in both systems)
Approach and tasks
1. We will watch the following video to understand how to calculate density of an element using
the periodic table and knowledge about the structure of the element.
Calculating mass from atomic information: https://www.youtube.com/watch?v=odcZBJ_eQrE
2. You will develop a pseudo-code for a program that will, based on user
input, determine the density of an element based on unit cell structure, atomic radius and
atomic mass.
3.  write a program that asks the user for necessary inputs and answers the original question. 

Unit cell resources:
https://courses.lumenlearning.com/cheminter/chapter/unit-cells/
Face Centered Cubic (FCC) structure: (image)

**Basic Geometry for FCC (Face-Centered Cubic)**

**Description:**

This figure explains the geometric relationships within a face-centered cubic (FCC) structure, focusing on the relationship between the lattice parameter \( a \) and the atomic radius \( R \).

**Diagrams:**

1. **Cube Diagram:**
   - The FCC unit cell is illustrated with atoms positioned at each corner and in the center of each face of the cube.
   - The lattice parameter is represented by \( a \), which is the edge length of the cube.
   - The diagonal of the face is shown, which equals \( 2\sqrt{2}R \), where \( R \) is the atomic radius.

2. **Close-Packed Direction Diagram:**
   - A line connecting atoms along the close-packed direction within the unit cell is shown.
   - This line visually represents the closest atomic interaction, confirming that the geometric relationship along this direction is \( a = 2\sqrt{2}R \).

**Formulas and Concepts:**

- **Volume Calculation:**
  \[
  V_{\text{unit cell}} = a^3 = (2\sqrt{2}R)^3 = 16\sqrt{2}R^3
  \]

- **Geometry Properties:**
  - \( a = 2\sqrt{2}R \)
  - The unit cell comprises 4 atoms in total.
  - The coordination number (number of nearest neighbors) is 12.

This description highlights why the FCC structure is densely packed, explaining how geometric and spatial considerations influence material properties.
Transcribed Image Text:**Basic Geometry for FCC (Face-Centered Cubic)** **Description:** This figure explains the geometric relationships within a face-centered cubic (FCC) structure, focusing on the relationship between the lattice parameter \( a \) and the atomic radius \( R \). **Diagrams:** 1. **Cube Diagram:** - The FCC unit cell is illustrated with atoms positioned at each corner and in the center of each face of the cube. - The lattice parameter is represented by \( a \), which is the edge length of the cube. - The diagonal of the face is shown, which equals \( 2\sqrt{2}R \), where \( R \) is the atomic radius. 2. **Close-Packed Direction Diagram:** - A line connecting atoms along the close-packed direction within the unit cell is shown. - This line visually represents the closest atomic interaction, confirming that the geometric relationship along this direction is \( a = 2\sqrt{2}R \). **Formulas and Concepts:** - **Volume Calculation:** \[ V_{\text{unit cell}} = a^3 = (2\sqrt{2}R)^3 = 16\sqrt{2}R^3 \] - **Geometry Properties:** - \( a = 2\sqrt{2}R \) - The unit cell comprises 4 atoms in total. - The coordination number (number of nearest neighbors) is 12. This description highlights why the FCC structure is densely packed, explaining how geometric and spatial considerations influence material properties.
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