Advertisements
Advertisements
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?
Advertisements
उत्तर
Given:
Edge length (a) = 405 pm = 4.05 × 10−8 cm
Molar mass = 27 g mol−1
Density (ρ) = 2.7 g/cm3 = 2.7 g cm−3
To find: Nature of cubic unit cell
Formula: Density (ρ) = `(M n)/(a^3 N_A)`
Calculation: From the formula,
Density, ρ = `(M n)/(a^3 N_A)`
∴ `2.7 "g cm"^-3 = (27 "g mol"^-1 xx "n")/((4.05 xx 10^-8)^3 "cm"^3 xx 6.022 xx 10^23 "atom mol"^-1)`
∴ n = `(2.7 "g cm"^-3 xx (4.05 xx 10^-8)^3 "cm"^3 xx 6.022 xx 10^23 "atom mol"^-1)/(27 "g mol"^-1)`
= 4.00
∴ Number of atoms in unit cell = 4
Since the unit cell contains 4 atoms, it has a face-centred cubic (fcc) or ccp structure.
The nature of the given cubic unit cell is face-centred cubic (fcc) or ccp unit cell.
संबंधित प्रश्न
Give the percentage of empty space in bcc lattice.
Find the number of atoms in the fcc unit cell.
The pyranose structure of glucose is ____________.
Silver crystallises in fcc structure, if edge length of unit cell is 316.5 pm. What is the radius of silver atom?
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)
A metal crystallises in bcc unit cell with edge length 'a'. What will be the volume of one atom?
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?
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?
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 ______.
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]
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)
What is the density of potassium, if it has a bcc structure with edge length 4Å?
(Atomic mass of K = 39)
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.]
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 is base centred (or end-centred) unit cell?
The correct sequence of the atomic layers in cubic close packing is ______.
The total number of different primitive unit cells is ______.
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 a density of 19.2 g cm−3 if it forms an fcc structure [a3 × NA = 40 cm3 mol−1].
