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
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)
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 with reason sign conventions of ΔS in the following reaction
CO2(g) → CO2(g)
A face centred cube (FCC) consists of how many atoms? Explain
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)
An element 'X' (At. mass = 40 g mol-1) having f.c.c. the structure has unit cell edge length of 400 pm. Calculate the density of 'X' and the number of unit cells in 4 g of 'X'. (NA = 6.022 × 1023 mol-1)
Number of types of orthorhombic unit cell is ___________.
What is the total number of atoms per unit cell in a face-centered cubic structure?
Volume of unit cell occupied in face-centered cubic arrangement 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 substance forms face-centered cubic crystals. Its density is 1.984 g/cm3 and the length of the edge of the unit cell is 630 pm. Calculate the molar mass in g/mol?
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).
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 2p sub shell is:
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 ______.
In an ionic solid r(+) = 1.6 Å and r(−) = 1.864 Å. Use the radius ratio rule to the edge length of the cubic unit cell is ______ Å.
An element A (Atomic weight = 100) having bcc structure has a unit cell edge length 400 pm. The number of atoms in 10 g of A is ______ × 1022 unit cells.
The ratio of number of atoms present in a simple cubic, body-centred cubic and face-centred cubic structure are, respectively ______.
