Final answer:
The density of solid W is 19.3 g/cm³. To find the number of atoms per cm³, we calculate the volume of one unit cell of W and then multiply by the number of unit cells. The volume of one unit cell is found using the formula for the volume of a cube. The edge length of a unit cell is 3.165 Å.
Step-by-step explanation:
The density of solid W is given as 19.3 g/cm³. To calculate the number of atoms per cubic centimeter of W, we need to know the volume of one W atom. Since W adopts a body-centered cubic unit cell, each unit cell contains 2 atoms (1 atom in the center and 8 atoms at each corner). The volume of one unit cell can be calculated using the formula for the volume of a cube: volume = edge length³. Given that the edge length is 3.165 Å, we can convert it to cm and calculate the volume of one unit cell. Once we have the volume of one unit cell, we can calculate the number of unit cells per cubic centimeter of W.
The volume of one unit cell of W is (3.165 Å)³ = 31.152 ų. Converting this to cm³ gives us 3.1152 x 10⁻²³ cm³. To find the number of unit cells per cm³, we take the reciprocal of the volume of one unit cell: 1/(3.1152 x 10⁻²³ cm³) = 3.2054 x 10²² unit cells/cm³. Since each unit cell contains 2 atoms, the number of atoms per cm³ can be calculated by multiplying the number of unit cells by 2: 3.2054 x 10²² x 2 = 6.4108 x 10²² atoms/cm³.
The volume of one unit cell is given by the formula volume = edge length³. In this case, the edge length is 3.165 Å. To find the volume of one unit cell in cm³, we need to convert the edge length from Å to cm: 3.165 Å = 3.165 x 10⁻⁸ cm. Now, we can calculate the volume of one unit cell: (3.165 x 10⁻⁸ cm)³ = 3.1152 x 10⁻²³ cm³. The edge length of a unit cell is 3.165 Å, or 3.165 x 10⁻⁸ cm.