## Unit – V A |

## Solid State Problems :

### Type – I : To Find Density of Substance

- Silver crystallises in face centred cubic structure. The edge length of a unit cell is found to be 408.7 pm. Calculate the density of silver. (Ag = 108 g/mol)
- Copper crystallises in face centred cubic structure. The edge length of a unit cell is found to be 3.61 x 10
^{-8}cm. Calculate density of copper if molar mass of copper is 63.5 g/mol. - Determine density of caesium chloride which crystallises in bcc type structure with an edge length of 412.1 pm. The atomic mass of Cs and Cl are 133 and 35.5 respectively.
- A metal crystallises as fcc structure and the unit cell has a length of edge 3.72 x 10
^{-8}cm. Calculate the density of the metal. Given the atomic mass of metal as 68.5 g/mol. - Sodium crystallises in bcc structure. If the atomic radius of sodium is 186 pm. Find a) edge length b) volume of unit cell and c) density of sodium crystal. Atomic mass of sodium is 23 g/mol.

### Type – II : To Find Radius of an Atom

- Naturally occurring gold crystallises in face centred cubic structure and has a density of 19.3 g cm
^{-3}. Calculate the atomic radius of gold. (Au = 197 g/mol) - Sodium metal crystallises in the bcc structure with an edge length of unit cell 4.29 x 10
^{-8}cm. Calculate the radius of sodium metal. - Niobium crystallises in bcc structure and has a density of 8.55 g cm
^{-3}. Calculate its atomic radius, if its atomic mass is 93. - Face centred cubic crystal lattice of copper has a density of 8.966 g cm
^{-3}. Calculate the volume of the unit cell. Given the molar mass of copper 63.5 g/mol and Avogadro’s number 6.022 x 1023 per mol. - Silver crystallises as fcc structure. If the density of silver is 10.51 g cm
^{-3}. calculate the volume of a unit cell. Given: molar mass of silver 108 g/mol. - Sodium metal crystallises in body centred cubic unit cell. If the distance between nearest Na atom is 368 pm, calculate the edge length of the unit cell.
- Copper crystallises in fcc structure. If two neighbouring Cu atoms are at a distance of 234 pm, find a) edge length, b) volume of a unit cell. Also find the distance between next neighbouring atoms.
- A metal occurs as body centred cube and has density 7.856 g cm
^{-3}. Calculate the atomic radius of metal. Atomic mass of metal = 58 g/mol.

### Type – III : To Find Molecular or Atomic Mass

- copper crystallises in fcc type unit cell. The edge length of a unit cell is 360.8 pm. The density of metallic copper is 8.92 g cm
^{-3}. Determine atomic mass of copper. - Silver crystallises in fcc type unit cell. The edge length of a unit cell is 4.07 10
^{-8}cm. The density of metallic silver is 10.5 g cm^{-3}. Determine atomic mass of silver.

### Type – IV : To Find Number of Atoms, Unit Cells and Type of Crystal Lattice

- An element germanium crystallises in bcc type crystal structure with an edge of unit cell 288 pm and the density of the element is 7.2 g cm
^{-3}. Calculate the number atoms present in 52 g of the crystalline element. Also ,calculate atomic mass of the element. - An atom crystallises in fcc crystal lattice and has a density of 10 g cm
^{-3}with unit cell edge length of 100 pm. Calculate the number atoms present in 1 g of the crystal. - Calculate the number of atoms present in 2 gram of crystal which has a face centred cubic crystal lattice having an edge length of 100 pm and density 10 g cm
^{-3}. - 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 crystal lattice. Given the molar mass of iron 56 g/mol. - The edge length of a unit cell of a cubic crystal is 4.3 A°, having atomic mass 89 g/mol. If the density of crystal is 9.02 g cm
^{-3}, find the number of atoms in a unit cell. - The density of silver having atomic mass 107.8 g /mol is 10.7 g cm
^{-3}. If edge length of a cubic unit cell is 405 pm, find the number of silver atoms in a unit cell and predict its type. - Aluminium having atomic mass 27 g/mol, crystallises in face centred cubic structure. Find number of aluminium atom in 10 g of it. Also find number of unit cells in the given quantity.

## Solution to Above Problems

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