Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
Given:
Density (d) = 10.8 g cm-3
Edge length (a) = 4.05 x 10- 8 cm
Molar mass = 107.8 g mol-1
Avogadro's number (NA) = 6.022 x 1023
To find:
Number of atoms in the unit cell
Formula:
a. Mass of one atom = `"Atomic mass"/"Avogadro number"`
b. Volume of unit cell = a3
c. Density = `"Mass of unit cell"/"Volume of unit cell"`
Calculation:
a) Mass of one Ag atom = `"Atomic mass of Ag"/"Avogadro number"`
Avogadro number
= `107.8/(6.022 xx 10^23)`
= 1.79 x 10-22 g
b) Volume of unit cell = a3
= ( 4.05 x 10-8 )3
= 6.64 x 10-23 cm3
c)
Density (d) = `"Mass of unit cell"/"Volume of unit cell"`
= `"Number of atoms in unit cell x Mass of one atom"/"Volume of unit cell"`
10.8 = `("Number of atoms in unit cell" xx 1.79 xx 10^-22)/(6.64 xx 10^-23)`
Number of atoms in unit cell = `( 10.8 xx 6.64 xx 10^-23)/( 1.79 xx 10^-22)`
= 40.06 x 10-1 = 4.0 ≈ 4
∴ The number of atoms in the unit cell of silver is 4.
APPEARS IN
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.
How many atoms constitute one unit cell of a face-centered cubic crystal?
Gold occurs as face centred cube and has a density of 19.30 kg dm-3. Calculate atomic radius of gold. (Molar mass of Au = 197)
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 Hexagonal and monoclinic unit cells
Distinguish between Face-centred and end-centred unit cells.
Explain how much portion of an atom located at (i) corner and (ii) body-centre of a cubic unit cell is part of its neighbouring unit cell.
How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.
Calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a f.c.c. structure. (Atomic mass of Al = 27 g mol–1)
The number of atoms per unit cell in a body centered cubic structure is ____________.
An atom located at the body center of a cubic unit cell is shared by ____________.
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 number of atoms contained in a fcc unit cell of a monoatomic substance is ____________.
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:
The density of a metal which crystallises in bcc lattice with unit cell edge length 300 pm and molar mass 50 g mol−1 will be:
The correct set of quantum numbers for 3d subshell is
The coordination number for body center cubic (BCC) system is
If a represents the edge length of the cubic systems, i.e. simple cubic, body centred cubic and face centered cubic, then the ratio of the radii of the sphere in these system will be:-
A solid is formed by 2 elements P and Q. The element Q forms cubic close packing and atoms of P occupy one-third of tetrahedral voids. The formula of the compound is ______.
