Example: Calculate the theoretical density of Al; Lattice parameter, a=4.05stackrel (circ )(A) Arrangement: FCC. Atomic weight of Al is 26.98g/mol Example: Calculate the density of solid crystalline BCC chromium (51.9g/mol) in gram/cm^3 Given r=128 pm

Question

Pertanyaan

Example: Calculate the theoretical density of Al; Lattice parameter, a=4.05stackrel (circ )(A) Arrangement: FCC. Atomic weight of Al is 26.98g/mol Example: Calculate the density of solid crystalline BCC chromium (51.9g/mol) in gram/cm^3 Given r=128 pm

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Answer 1

\[ \rho = \frac{4 \cdot 26.98}{6.022 \times 10^{23} \cdot (4.05 \times 10^{-8})^3} \]
\[ \rho \approx 2.70 \, \text{g/cm}^3 \]

Contoh 2: Calculate the density of solid crystalline BCC chromium \( (51.9 \, \text{g/mol}) \) in \( \text{gram/cm}^3 \)

*Given:*
- \( r = 128 \, \text{pm} \)

Penjelasan:

For a BCC lattice, the relationship between the lattice parameter \( a \) and the atomic radius \( r \) is:
\[ a = \frac{4r}{\sqrt{3}} \]

The density (\( \rho \)) can be calculated using the formula:
\[ \rho = \frac{Z \cdot A}{N_A \cdot a^3} \]
where:
- \( Z \) is the number of atoms per unit cell (BCC: \( Z = 2 \))
- \( A \) is the atomic weight
- \( N_A \) is Avogadro's number (\( 6.022 \times 10^{23} \))
- \( a \) is the lattice parameter

Jawaban:**

First, calculate \( a \):
\[ a = \frac{4 \cdot 128 \, \text{pm}}{\sqrt{3}} \approx 295.84 \, \text{pm} \]

Then, calculate the density:
\[ \rho = \frac{2 \cdot 51.9}{6.022 \times 10^{23} \cdot (295.84 \times 10^{-10})^3} \]
\[ \rho \approx 7.19 \, \text{g/cm}^3 \]

Answer 2

Density (\( \rho \)) for a FCC lattice can be calculated using the formula:
\[ \rho = \frac{Z \cdot A}{N_A \cdot a^3} \]
where:
- \( Z \) is the number of atoms per unit cell (FCC: \( Z = 4 \))
- \( A \) is the atomic weight
- \( N_A \) is Avogadro's number (\( 6.022 \times 10^{23} \))
- \( a \) is the lattice parameter

Pertanyaan

Example: Calculate the theoretical density of Al; Lattice parameter, a=4.05stackrel (circ )(A) Arrangement: FCC. Atomic weight of Al is 26.98g/mol Example: Calculate the density of solid crystalline BCC chromium (51.9g/mol) in gram/cm^3 Given r=128 pm

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