Advertisements
Advertisements
प्रश्न
The unit cell of Na is bcc and its density is 0.97 g/cm3. What is the radius of a sodium atom if the molar mass of Na is 23 g/mol?
उत्तर
Given: Density = 0.97 g/cm3, Molar mass (M) = 23 g/mol
To find: Radius of sodium atom (r)
Formula:
1. Density (ρ) = `"M n"/("a"^3 "N"_"A")`
2. For bcc unit cell, r = `(sqrt3 "a")/4`
Calculation: For a bcc lattice, number of atoms per unit cell is 2.
∴ n = 2
From formula (i),
`"a"^3 = "M n"/(rho "N"_"A")`
`"a"^3 = (23 "g mol"^-1 xx 2 "atom")/(0.97 "g cm"^-3 xx 6.022 xx 10^23 "atom mol"^-1) = 7.875 xx 10^-23 "cm"^3`
a = `root(3)(7.875 xx 10^-23 "cm"^3) = 4.286 xx 10^-8`cm
From formula (ii),
r = `(sqrt3 "a")/4 = (sqrt3 xx 4.286 xx 10^-8)/4 = 1.86 xx 10^-8` cm
Radius of sodium atom is 1.86 × 10-8 cm.
संबंधित प्रश्न
The unit cell of a simple cubic system has atoms at the eight corners. Hence, number of atoms in a unit cell is ______.
In crystal lattice formed by primitive unit cell, the space occupied by particles is ______.
Write the effect on density of a substance in the Frenkel defect?
Name the bravais lattice in the triclinic system.
Draw diagram of bcc unit cell.
If a metal crystallises in bcc structure with edge length of unit cell 4.29 × 10-8 cm the radius of metal atom is ______.
Which of the following crystal systems shows base-centred unit cell?
Sodium crystallizes in bee structure with radius 1.86 × 10-8 cm. Calculate the edge length of unit cell.
What is the mass of unit cell of gold if it crystallises in fee structure?
(At mass of gold= 197 g mol-1)
The edge length of bcc type of unit cell of an element is 400 pm. Calculate the density of unit cell. (Molar mass of an element = 100 g mol-1)
What is the number of atoms present per unit cell of aluminium having edge length 4 Å?
How much part of an atom occupies each comer of bee unit cell?
Which is the number of atoms in 12.08 × 1023 unit cells if an element crystallizes in bcc structure?
A metallic element crystallizes to bcc type of crystal lattice, having edge length of unit cell 5 A. Calculate radius of its atom.
Bcc type of crystal lattice contains 1.208 × 1023 unit cells. How many atoms of the element are present in these unit cells?
An element crystallizes in fee lattice with cell edge 250 pm. Calculate the density of an element. (At. Mass = 90.3)
Xenon crystallizes in fee lattice and the edge length of unit cell is 620 pm. What is the radius of Xe atom?
The edge length of bcc type of unit cell of metal is 5 Å. What is the radius of metal atom if it's density is 2 glee?
Find the molar mass of an element that crystallises forming unit cell structure having edge length 4 × 10-8 cm and containing 4 particles. (ρ = 19.7 g cm-3).
How many particles are present per bcc unit cell?
