Advertisements
Advertisements
प्रश्न
How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.
Advertisements
उत्तर
Suppose, the edge length of the unit cell = a
Number of atoms present per unit cell = Z
Atomic mass of the element = M
For a cubic unit cell,
Volume of the unit cell = a3 ...(i)
Density of the unit cell
ρ' = `"Mass of unit cell"/"Volume of unit cell"` ...(ii)
Mass of unit cell = Number of atoms per unit cell × Mass of one atom
= Z × m ...(iii)
where m is the mass of a single atom. This is given by
`m = "Atomic mass"/"Avogadro’s number"`
`m = M/N_A` ...(iv)
Substituting the value of m in eq. (iii), we have
Mass of unit cell = `Z xx M/N_A`
Substituting the corresponding values in eq. (ii), the density of the unit cell (ρ') is given by
ρ' = `"Mass of unit cell"/"Volume of unit cell"`
ρ' = `(Z xx M/N_A)/a^3`
or, ρ' = `(Z xx M)/(a^3 xx N_A)`
The density of a crystal (ρ) is the same as the density of its unit cell (ρ'), i.e., ρ' = ρ. Therefore the density ρ of a crystal is given by
`rho = (Z xx M)/(a^3 xx N_A)`
∴ `M = (rho xx a^3 xx N_A)/(Z)`
संबंधित प्रश्न
A unit cell of iron crystal has edge length 288 pm and density 7.86 g.cm-3. Find the number of atoms per unit cell and type of the crystal lattice.
Given : Molar mass of iron = 56 g.mol-1; Avogadro's number NA = 6.022 x 1023.
Face centred cubic crystal lattice of copper has density of 8.966 g.cm-3. Calculate the volume of the unit cell. Given molar mass of copper is 63.5 g mol-1 and Avogadro number NA is 6.022 x 1023 mol-1
An element crystallises in a b.c.c lattice with cell edge of 500 pm. The density of the element is 7.5g cm-3. How many atoms are present in 300 g of the element?
An element with molar mass 27 g mol−1 forms a cubic unit cell with edge length 4.05 ✕ 10−8 cm. If its density is 2.7 g cm−3, what is the nature of the cubic unit cell?
Distinguish between Face-centred and end-centred unit cells.
An element with molar mass 2.7 × 10-2 kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 × 103 kg m−3, what is the nature of the cubic unit cell?
An element has atomic mass 93 g mol−1 and density 11.5 g cm–3. If the edge length of its unit cell is 300 pm, identify the type of unit cell. (NA = 6.023 × 1023 mol−1)
The density of silver having an atomic mass of 107.8 g mol- 1 is 10.8 g cm-3. If the edge length of cubic unit cell is 4.05 × 10- 8
cm, find the number of silver atoms in the unit cell.
( NA = 6.022 × 1023, 1 Å = 10-8 cm)
The number of atoms per unit cell in a body centered cubic structure is ____________.
Volume of unit cell occupied in face-centered cubic arrangement is ____________.
TiCl has the structure of CsCl. The coordination number of the ions in TiCl is ____________.
An element forms a cubic unit cell with edge length 405 pm. Molar mass of this element is 2.7 × 10−2 kg/mol and its density is given as 2.7 × 103 kg/m3. How many atoms of these elements are present per unit cell?
A metal has a body-centered cubic crystal structure. The density of the metal is 5.96 g/cm3. Find the volume of the unit cell if the atomic mass of metal is 50.
An element (atomic mass 100 g/mol) having bcc structure has unit cell edge 400 pm. The density of element is (No. of atoms in bcc, Z = 2).
Edge length of unit cell of chromium metal is 287 pm with a bcc arrangement. The atomic radius is of the order:
The edge length of fcc cell is 508 pm. If the radius of cation is 110 pm, the radius of anion is:
Match the type of unit cell given in Column I with the features given in Column II.
| Column I | Column II |
| (i) Primitive cubic unit cell | (a) Each of the three perpendicular edges compulsorily have the different edge length i.e; a ≠ b ≠ c. |
| (ii) Body centred cubic unit cell | (b) Number of atoms per unit cell is one. |
| (iii) Face centred cubic unit cell | (c) Each of the three perpendicular edges compulsorily have the same edge length i.e; a = b = c. |
| (iv) End centred orthorhombic cell | (d) In addition to the contribution from unit cell the corner atoms the number of atoms present in a unit cell is one. |
| (e) In addition to the contribution from the corner atoms the number of atoms present in a unit cell is three. |
The correct set of quantum numbers for 3d subshell is
Percentage of free space in body centred cubic unit cell is
The ratio of number of atoms present in a simple cubic, body-centred cubic and face-centred cubic structure are, respectively ______.
