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?
Advertisements
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 following crystal systems contain 4 Bravais lattices?
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.
Which among the following crystal lattices occupies all of the cubic holes by cations?
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.
How many unit cells are present in 1.00 cm3 of of aluminum crystal, if edge length of unit cell is 3.54 × 10-8 cm?
What is the mass of unit cell of gold if it crystallises in fee structure?
(At mass of gold= 197 g mol-1)
How many lithium atoms are present in a unit cell with edge length 3.5 Å and density 0.53 g cm-3 (At. mass of Li= 6.94).
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.
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?
An element having an atomic radius of 0.14 nm crystallizes in an fcc unit cell. What is the length of a side of the cell?
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).
What is the number of different types of unit cells present in tetragonal crystal system?
