Advertisements
Advertisements
Questions
Obtain the relationship between the density of a substance and the edge length of the unit cell.
Derive the relationship between molar mass, density of the substance and unit cell edge length.
Advertisements
Solution
If the edge length of the cubic unit cell is ‘a’, then the volume of the unit cell is a3.
Suppose that mass of one particle is 'm’ and that there are ‘n’ particles per unit cell.
∴ Mass of unit cell = m × n ...(1)
The density of unit cell (ρ), which is same as density of the substance is given by:
`rho = "Mass of unit cell"/"Volume of unit cell" = ("m" xx "n")/"a"^3` = Density of substance …(2)
Molar mass (M) of the substance is given by:
M = mass of one particle × number of particles per mole
= m × NA (NA is Avogadro number)
Therefore, m = `"M"/"N"_"A"` ...(3)
Combining equations (1) and (3), gives
`rho = "n M"/("a"^3 "N"_"A")` ...(4)
RELATED QUESTIONS
Write the relationship between radius of atom and edge length of fcc unit cell.
Give the percentage of empty space in bcc lattice.
If the total volume of a simple cubic unit cell is 6.817 × 10-23 cm3, what is the volume occupied by particles in the unit cell?
Find the number of atoms in the fcc unit cell.
Derive the relationship between density of substance, its molar mass, and the unit cell edge length. Explain how you will calculate the number of particles, and a number of unit cells in x g of metal.
An element crystallizes in fcc type of unit cell. The volume of one unit cell is 24.99 × 10-24 cm3 and density of the element 7.2 g cm-3, Calculate the number of unit cells in 36 g of pure sample of element?
In bcc unit cell, the edge length (a) and radius of sphere (r) are related to each other by equation:
How many total constituent particles are present in simple cubic unit cell?
The number of atoms in 500 g of a fcc crystal of a metal with density d = 10 g/cm3 and cell edge 100 pm, is equal to ____________.
If the edge of a body-centred unit cell is 360 pm, what will be the approximate radius of the atom present in it? (in pm)
Which of the following formulae is used to find edge length of bee unit cell?
What is the density of iron crystal which crystallizes in body-centred cubic structure with edge length 287 pm? (At. mass of Fe = 56 amu)
The coordination number of atoms in body-centred cubic structure (bcc) is ______.
An element has a bee structure with unit cell edge length of 288 pm. How many unit cells and number of atoms are present in 200 g of the element?
A metal has an fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm−3. The molar mass of the metal is ______.
(NA Avogadro's constant = 6.02 × 1023 mol−1)
In face centred cubic unit cell, what is the volume occupied?
Calculate the density of metal with molar mass 56 g mol- 1 that crystallises to form a bcc structure with edge length 288 pm.
An element with molar mass 2.7 × 10-2 kg/mol. Forms a cubic units cell with edge length of 405 pm. If the density is 2.7 × 103 kg/m3. Find the nature of a cubic unit cell.
At room temperature, polonium Crystallises in a primitive cubic unit cell. If a = 3.36 Å. Calculate the theoretical density of polonium. [It's atomic weight is 209 g/mol.]
The correct sequence of the atomic layers in cubic close packing is ______.
What would be the empirical formula of a compound having a unit cell containing A ion shared equally at the corner of the cube and B ion on the centre of faces of the cube?
The number of particles present in Face Centred Cubic Unit cell is/are ______.
Which of the following metals exhibits minimum packing efficiency in its cubic system?
The cubic unit cell of a metal (molar mass = 63.55g mol−1) has an edge length of 362 pm. Its density is 8.92g cm−3.
The type of unit cell is ______.
Calculate the molar mass of an element having density 2.8 g cm−3 and forms fcc unit cell.
[a3.NA = 38.5 cm3 mol−1]
