Advertisements
Advertisements
Question
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
Solution
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.
RELATED QUESTIONS
Obtain the relationship between the density of a substance and the edge length of the unit cell.
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?
Calculate the number of unit cells in 0.3 g of a species having density of 8.5 g/cm3 and unit cell edge length 3.25 × 10-8 cm.
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.
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?
In bcc unit cell, the edge length (a) and radius of sphere (r) are related to each other by equation:
A metal crystallises in bcc unit cell with edge length 'a'. What will be the volume of one atom?
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?
Copper and silver have ____________ crystal structure.
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?
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 ______.
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]
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?
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.
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 ______.
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 ______.
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].
