An element with body centred cubic structure.Edge length is 400pm.Calculate the density of element.Atomic Mass of element is 100u?
(2*100/6.02E23) = mass unit cell.
Volume = (edge length)^3
Then density = mass/volume.
To calculate the density of an element, we need to find its mass and volume.
1. Mass calculation:
The atomic mass given is 100 u (atomic mass units). Since the molar mass of an element is the mass of one mole of its atoms, we can say that 1 mole of this element weighs 100 grams.
2. Volume calculation:
In a body-centered cubic (BCC) structure, there is one atom at each of the eight corners of the cube, and one atom at the center of the cube (total = 2 atoms per unit cell).
The edge length given is 400 pm (picometers).
To calculate the volume of the unit cell (V), we use the formula:
V = a^3, where a is the edge length.
Converting the edge length from picometers to meters:
400 pm = 400 x 10^-12 m = 4 x 10^-10 m
V = (4 x 10^-10 m)^3 = 64 x 10^-30 m^3
3. Density calculation:
Density (ρ) of a substance is defined as the mass per unit volume:
ρ = mass / volume
Since we know the mass of 1 mole of the element is 100 grams, we can convert it to kilograms (kg):
mass = 100 grams = 0.1 kg
ρ = mass / volume
ρ = 0.1 kg / 64 x 10^-30 m^3
Now, we can calculate the density.
Using scientific notation:
ρ = 1.56 x 10^3 kg/m^3
Therefore, the density of the element with a body-centered cubic structure is approximately 1.56 x 10^3 kg/m^3.