The element rubidium has bcc packing with a body-centered cubic unit cell. The density of Rb is 1530 kg/m3. Calculate the volume (L) of the unit cell of rubidium.
Molar mass of Rb=85.468.
Since it is bcc, it would have 2 atoms/unit cell.
Can you please help me solve this? Thank you.
Sure! To calculate the volume of the unit cell of rubidium, we can use the formula:
Volume of the unit cell = (molar mass of Rb / Avogadro's number) / density
First, let's find Avogadro's number. Avogadro's number is the number of atoms or molecules per mole, and it is approximately equal to 6.022 x 10^23.
Now, let's plug in the values into the formula:
Volume = (85.468 g/mol / 6.022 x 10^23) / 1530 kg/m^3
To convert from grams to kilograms, divide by 1000. So, the molar mass in kg/mol is 0.085468 kg/mol.
Now we have:
Volume = (0.085468 kg/mol / 6.022 x 10^23) / 1530 kg/m^3
Simplifying this, we get:
Volume = (0.085468 kg / (6.022 x 10^23)) / 1530 kg/m^3
Canceling out the units, we have:
Volume = (0.085468 / 6.022 x 10^23) / 1530 m^3
Now, divide the numerator by the denominator:
Volume = 1.407 x 10^-26 m^3
So, the volume of the unit cell of rubidium is approximately 1.407 x 10^-26 m^3.
Sure! To calculate the volume of the unit cell of rubidium (Rb) in body-centered cubic (bcc) packing, we can use the following formula:
Volume of unit cell (V) = (1/2) * (a)^3
Where "a" is the edge length of the unit cell.
Given that rubidium has a molar mass of 85.468 g/mol, and the density of Rb is 1530 kg/m^3, we can calculate the edge length "a" using the following steps:
Step 1: Convert the molar mass of Rb to kg/mol.
molar mass of Rb = 85.468 g/mol = 0.085468 kg/mol
Step 2: Calculate the number of moles in 1 cubic meter of Rb.
density of Rb = 1530 kg/m^3
number of moles = density / molar mass
number of moles = 1530 kg/m^3 / 0.085468 kg/mol = 17917.63 mol/m^3
Step 3: Determine the number of unit cells per cubic meter.
In a bcc structure, there are 2 atoms per unit cell.
Therefore, the number of unit cells per cubic meter is equal to half the number of moles.
number of unit cells = (1/2) * 17917.63 mol/m^3 = 8958.82 unit cells/m^3
Step 4: Calculate the edge length "a" using the relationship between the volume of a cube and the number of unit cells per cubic meter.
Volume of unit cell (V) = (1/2) * (a)^3
a = (2 * V / 1)^(1/3)
a = (2 * (1 / number of unit cells) / 1)^(1/3)
a = (2 / number of unit cells)^(1/3)
a = (2 / 8958.82)^(1/3)
a ≈ 4.18 x 10^-8 m
Therefore, the volume of the unit cell of rubidium is approximately 4.18 x 10^-8 m.