Advertisements
Advertisements
Question
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
Solution
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)`
APPEARS IN
RELATED QUESTIONS
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.
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?
Explain with reason sign conventions of ΔS in the following reaction
CO2(g) → CO2(g)
Number of types of orthorhombic unit cell 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).
Sodium metal crystallises in a body-centred cubic lattice with a unit cell edge of 4.29 Å. The radius of the sodium atom is approximately ______.
The empty space in the body-centered cubic lattice is ____________.
The number of atoms contained in a fcc unit cell of a monoatomic substance is ____________.
Which of the following metal(s) show(s) hexagonal close-packed structure (hcp) and which show face-centered cubic (fcc) structure?
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 ratio of number of atoms present in a simple cubic, body-centred cubic and face-centred cubic structure are, respectively ______.
