Advertisements
Advertisements
प्रश्न
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.
उत्तर
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)
संबंधित प्रश्न
Answer the following in brief.
Calculate the number of atoms in fcc unit cell.
An element with molar mass 27 g/mol forms a cubic unit cell with edge length of 405 pm. If the density of the element is 2.7 g/cm3, what is the nature of the cubic 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?
What is the percentage of unoccupied space in fcc unit cell?
An element (atomic mass M g/mol) having bcc structure has unit cell edge 400 pm. The density of the element is ____________ g/cm3.
[NA = 6.0 × 1023 atom mol−1)
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)
An element crystallizes bcc type of unit cell, the density and edge length of unit cell is 4 g cm−3 and 500 pm respectively. What is the atomic mass of an element?
Consider the following unit cell.
The number of particles (spheres) per unit cell is:
A metallic element has a cubic lattice with edge length of unit cell 2 Å. Calculate the number of unit cells in 200 g of the metal, if density of metal is 2.5 g cm-3?
Which of the following formulae is used to find edge length of bee unit cell?
The coordination number of atoms in body-centred cubic structure (bcc) is ______.
Identify unit cell from following having four particles in it
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.
What is the density of potassium, if it has a bcc structure with edge length 4Å?
(Atomic mass of K = 39)
Silver crystallizes in the fcc structure. If the edge length of the unit cell is 400 pm, calculate the density of silver (Atomic mass of Ag = 108).
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 ______.
