If a body-centered cubic unit cell has a volume of 1.447 x 10° pm, what must be the dimension of the cube's edge? Selected Answer: O a. 1.131 x 10° pm Answers: 1.131 x 10° pm a. b. 110 pm 1.20 x 10* pm C. O d. 525 pm 367 pm e.
If a body-centered cubic unit cell has a volume of 1.447 x 10° pm, what must be the dimension of the cube's edge? Selected Answer: O a. 1.131 x 10° pm Answers: 1.131 x 10° pm a. b. 110 pm 1.20 x 10* pm C. O d. 525 pm 367 pm e.
Chemistry
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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:**
If a body-centered cubic unit cell has a volume of \(1.447 \times 10^{8} \, \text{pm}^3\), what must be the dimension of the cube's edge?
**Answers Provided:**
- a. \(1.131 \times 10^{8} \, \text{pm}\)
- b. \(110 \, \text{pm}\)
- c. \(1.20 \times 10^{4} \, \text{pm}\)
- d. \(525 \, \text{pm}\)
- e. \(367 \, \text{pm}\)
**Selected Answer:**
a. \(1.131 \times 10^{8} \, \text{pm}\) *(marked incorrect)*
**Correct Answer:**
d. \(525 \, \text{pm}\)
### Explanation:
For a body-centered cubic (BCC) unit cell, the relationship between the edge length \(a\) and the volume \(V\) is given by:
\[ V = a^3 \]
To find the edge length \(a\), we take the cube root of the volume:
\[ a = \sqrt[3]{V} \]
Given:
\[ V = 1.447 \times 10^{8} \, \text{pm}^3 \]
Calculating \(a\):
\[ a = \sqrt[3]{1.447 \times 10^{8}} \, \text{pm} \]
Therefore:
\[ a \approx 525 \, \text{pm} \]
Thus, the correct answer is \(525 \, \text{pm}\) which corresponds to option d.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7e0b628-1887-4036-8cfa-486903c53c1e%2F0c1ec6e7-f92b-4283-909c-c23f48265d91%2Fr12sq87_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
If a body-centered cubic unit cell has a volume of \(1.447 \times 10^{8} \, \text{pm}^3\), what must be the dimension of the cube's edge?
**Answers Provided:**
- a. \(1.131 \times 10^{8} \, \text{pm}\)
- b. \(110 \, \text{pm}\)
- c. \(1.20 \times 10^{4} \, \text{pm}\)
- d. \(525 \, \text{pm}\)
- e. \(367 \, \text{pm}\)
**Selected Answer:**
a. \(1.131 \times 10^{8} \, \text{pm}\) *(marked incorrect)*
**Correct Answer:**
d. \(525 \, \text{pm}\)
### Explanation:
For a body-centered cubic (BCC) unit cell, the relationship between the edge length \(a\) and the volume \(V\) is given by:
\[ V = a^3 \]
To find the edge length \(a\), we take the cube root of the volume:
\[ a = \sqrt[3]{V} \]
Given:
\[ V = 1.447 \times 10^{8} \, \text{pm}^3 \]
Calculating \(a\):
\[ a = \sqrt[3]{1.447 \times 10^{8}} \, \text{pm} \]
Therefore:
\[ a \approx 525 \, \text{pm} \]
Thus, the correct answer is \(525 \, \text{pm}\) which corresponds to option d.
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