The element niobium has bcc packing with a body-centered cubic unit cell. The volume of the unit cell is 3.59 x 10-26 L. Calculate the density (g/cm3) of the element
In each cell the number of atoms is:
1 center
1/8 of each corner, or 1/8 *8 total atoms=1 atom
density=mass of 2 atoms Noibium/volume
To calculate the density of an element, we need to know its molar mass and the volume of the unit cell.
Step 1: Determine the molar mass of niobium (Nb). The molar mass of niobium is approximately 92.91 g/mol.
Step 2: Convert the volume of the unit cell from liters to cm³.
Given volume = 3.59 x 10^(-26) L
Since 1 L is equal to 1000 cm³, we can convert the given volume as follows:
Volume = 3.59 x 10^(-26) L x 1000 cm³/L
Step 3: Calculate the number of unit cells in 1 cm³.
Since the unit cell in this case is a body-centered cubic (bcc), there is 1 niobium atom per unit cell.
To determine the number of unit cells in 1 cm³, we need to calculate the volume of one unit cell:
Volume of unit cell = Volume / Number of unit cells in 1 cm³
Step 4: Calculate the number of moles in one unit cell.
To calculate the number of moles in one unit cell, we divide the volume of one unit cell by Avogadro's number (6.022 x 10^23):
Number of moles = Volume of unit cell / Avogadro's number
Step 5: Calculate the mass of one unit cell.
The mass of one unit cell is equal to the molar mass of niobium multiplied by the number of moles:
Mass of one unit cell = Number of moles x Molar mass
Step 6: Calculate the density.
Density is defined as the mass per unit volume. We can calculate the density using the formula:
Density = Mass of one unit cell / Volume of one unit cell
Finally, plug in the values calculated in the previous steps to calculate the density of niobium.