The radius of a single atom of a generic element X is 167 pm and a crystal of X has a unit cell that is a simple cubic. Calculate the volume of the unit cell. volume: m
The radius of a single atom of a generic element X is 167 pm and a crystal of X has a unit cell that is a simple cubic. Calculate the volume of the unit cell. volume: m
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Problem Statement:**
The radius of a single atom of a generic element X is 167 pm, and a crystal of X has a unit cell that is a simple cubic. Calculate the volume of the unit cell.
**Calculation:**
- **Formula:** In a simple cubic structure, the edge length \(a\) of the cube is twice the atomic radius.
\[
a = 2 \times \text{radius} = 2 \times 167 \, \text{pm} = 334 \, \text{pm}
\]
- **Convert pm to meters:** \(334 \, \text{pm} = 334 \times 10^{-12} \, \text{meters}\).
- **Volume of the cube:**
\[
V = a^3 = (334 \times 10^{-12})^3 \, \text{m}^3
\]
**Solution Box:**
- **Volume:** [ ] m\(^3\)
**Instructions:**
Insert your answer in the box above after performing the cubic calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3c0899a-5c62-4a86-a39c-5b160af6a916%2F583566a6-8249-4bd0-8852-6827785b8209%2Fsr6qfd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The radius of a single atom of a generic element X is 167 pm, and a crystal of X has a unit cell that is a simple cubic. Calculate the volume of the unit cell.
**Calculation:**
- **Formula:** In a simple cubic structure, the edge length \(a\) of the cube is twice the atomic radius.
\[
a = 2 \times \text{radius} = 2 \times 167 \, \text{pm} = 334 \, \text{pm}
\]
- **Convert pm to meters:** \(334 \, \text{pm} = 334 \times 10^{-12} \, \text{meters}\).
- **Volume of the cube:**
\[
V = a^3 = (334 \times 10^{-12})^3 \, \text{m}^3
\]
**Solution Box:**
- **Volume:** [ ] m\(^3\)
**Instructions:**
Insert your answer in the box above after performing the cubic calculation.
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