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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.
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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
An element with molar mass 27 g/mol forms a cubic unit cell with edge length of 405 p.m. 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.
Find the number of atoms in the fcc unit cell.
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?
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 ____________.
Sodium crystallizes in bcc structure with radius 1.86 × 10−8 cm. What is the length of unit cell of sodium?
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?
An element with density 2.8 g cm−3 forms fcc unit cell having edge length 4 × 10−8 cm. Calculate molar mass of the element.
Copper and silver have ____________ crystal structure.
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 number of atoms in 100 g of an fcc crystal with density 10 g cm-3 and unit cell edge length 200 pm is equal to ______.
Gold crystallises into face-centred cubic cells. The edge length of a unit cell is 4.08 × 10–8 cm. Calculate the density of gold. [Molar mass of gold = 197 g mol–1]
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).
The total number of different primitive unit cells 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?
An element crystallises in fee structure. If molar mass of element is 72.7 g mol -1, the mass of its one unit cell will be ______.
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?
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]
Calculate the molar mass of an element having a density of 19.2 g cm−3 if it forms an fcc structure [a3 × NA = 40 cm3 mol−1].
