- Body-Centered Cubic (BCC) Please draw it: The number of atoms per unit cell: atoms/unit cell - Face-Centered Cubic (FCC) Please draw it: The number of atoms per unit cell: atoms/unit cell Atomic Arrangements in Crystals Atomic arrangements affect the properties of solids such as the density of metals. The density of metals can be calculated using the lattice parameter and the number of atoms per unit cell. =number of atoms in the unit cell " atoms" =Molar Mass (atomic weight) ''g/mol'' =volume of unit cell =Avogadro's number (6.023times 10^23 atoms /mol)

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- Body-Centered Cubic (BCC) Please draw it: The number of atoms per unit cell: atoms/unit cell - Face-Centered Cubic (FCC) Please draw it: The number of atoms per unit cell: atoms/unit cell Atomic Arrangements in Crystals Atomic arrangements affect the properties of solids such as the density of metals. The density of metals can be calculated using the lattice parameter and the number of atoms per unit cell. =number of atoms in the unit cell " atoms" =Molar Mass (atomic weight) ''g/mol'' =volume of unit cell =Avogadro's number (6.023times 10^23 atoms /mol)

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Answer 1

1. Body-Centered Cubic (BCC):

In a BCC structure, there is one atom at each corner of the cube and one atom at the center of the cube. Each corner atom is shared among 8 adjacent unit cells, so only 1/8 of each corner atom belongs to the unit cell. Therefore, the number of atoms per unit cell in a BCC structure is:

\[ \text{Number of atoms per unit cell} = 1 + 8 \times \frac{1}{8} = 2 \text{ atoms/unit cell} \]

2. Face-Centered Cubic (FCC):

In an FCC structure, there is one atom at each corner of the cube and one atom at the center of each face of the cube. Each corner atom is shared among 8 adjacent unit cells, and each face-centered atom is shared among 2 adjacent unit cells. Therefore, the number of atoms per unit cell in an FCC structure is:

\[ \text{Number of atoms per unit cell} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \text{ atoms/unit cell} \]

Atomic Arrangements in Crystals:

The atomic arrangements significantly affect the properties of solids, including the density of metals. The density of metals can be calculated using the lattice parameter and the number of atoms per unit cell.

The formula for calculating the density (\( \rho \)) of a metal is:

\[ \rho = \frac{\text{number of atoms in the unit cell} \times \text{Molar Mass (atomic weight)} }{\text{Volume of the unit cell} \times \text{Avogadro's number}} \]

Where:
- Number of atoms in the unit cell: \( N \)
- Molar Mass (atomic weight): \( M \)
- Volume of the unit cell: \( V \)
- Avogadro's number: \( N_A = 6.023 \times 10^{23} \text{ atoms/mol} \)

This formula allows you to determine the density of metals based on their atomic structure and molar mass.

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