Length of the edge , a = 290 pm =290 x 10-10 cm Volume of unit cell = ( 290 x 10-10 cm )3 = 24.39 x 10-24 cm3 Since it is bcc arrangement, Number of atoms in the unit cell, Z = 2 Atomic mass of the element = 50 Mass of the atom = atomic mass/ Avogadro number = M/No = 50/6.02 x 1023 Mass of the unit cell = Z x M/No = 2 x 50/6.02 x 1023 = 100/6.23 x 1023 Therefore , density = mass of unit cell / volume of unit cell = 100/6.023 x 1023 x 24.39 x 10-24 = 6.81 g cm-3

Density of a BCC Unit Cell

To calculate the density of a body-centered cubic (BCC) unit cell, we need to determine the mass and volume of the unit cell. Given that the atomic mass of the element is 50 and the edge length of the unit cell is 290 pm, we can follow these steps:

Finding the Volume of the BCC Unit Cell
1. Convert the edge length from picometers (pm) to centimeters (cm):
290 pm = 290 x 10^-10 cm

2. The volume of a BCC unit cell can be found using the formula:
V = (a^3) * (8r), where a is the edge length and r is the radius of the atom.

3. To find the radius of the atom, we can use the relationship between the atomic mass and the atomic radius. However, this information is not given in the question. Therefore, we need to make some assumptions or use a known value for the element.

Assumption: Let's assume the element is iron (Fe), which has a known atomic radius of approximately 0.124 nm (1 nm = 10 Å = 10^-7 cm). Converting this to cm:
r = 0.124 nm = 0.124 x 10^-7 cm

4. Plug in the values into the formula to calculate the volume:
V = (290 x 10^-10 cm)^3 * (8 * 0.124 x 10^-7 cm)

Finding the Mass of the BCC Unit Cell
5. The mass of the BCC unit cell is equal to the atomic mass of the element multiplied by the number of atoms per unit cell.

6. In a BCC unit cell, there are 2 atoms, so the mass of the unit cell can be calculated as:
Mass = 2 * atomic mass

Calculating the Density
7. Finally, the density can be calculated by dividing the mass by the volume:
Density = Mass / Volume

8. Plug in the values for mass and volume to calculate the density.

Final Answer: The calculated density will depend on the assumed element and its atomic radius. Make sure to include the assumptions and values used in the calculation.