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प्रश्न
Obtain the relationship between the density of a substance and the edge length of the unit cell.
Derive the relationship between molar mass, density of the substance and unit cell edge length.
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उत्तर
If the edge length of the cubic unit cell is ‘a’, then the volume of the unit cell is a3.
Suppose that mass of one particle is 'm’ and that there are ‘n’ particles per unit cell.
∴ Mass of unit cell = m × n ...(1)
The density of unit cell (ρ), which is same as density of the substance is given by:
`rho = "Mass of unit cell"/"Volume of unit cell" = ("m" xx "n")/"a"^3` = Density of substance …(2)
Molar mass (M) of the substance is given by:
M = mass of one particle × number of particles per mole
= m × NA (NA is Avogadro number)
Therefore, m = `"M"/"N"_"A"` ...(3)
Combining equations (1) and (3), gives
`rho = "n M"/("a"^3 "N"_"A")` ...(4)
संबंधित प्रश्न
Answer the following in brief.
Calculate the number of atoms in fcc unit cell.
Write the relationship between radius of atom and edge length of fcc unit cell.
Give the percentage of empty space in bcc lattice.
If the total volume of a simple cubic unit cell is 6.817 × 10-23 cm3, what is the volume occupied by particles in the unit cell?
Derive the relationship between density of substance, its molar mass, and the unit cell edge length. Explain how you will calculate the number of particles, and a number of unit cells in x g of metal.
Silver crystallises in fcc structure, if edge length of unit cell is 316.5 pm. What is the radius of silver atom?
An element crystallizes in fcc type of unit cell. The volume of one unit cell is 24.99 × 10-24 cm3 and density of the element 7.2 g cm-3, Calculate the number of unit cells in 36 g of pure sample of element?
An element (atomic mass M g/mol) having bcc structure has unit cell edge 400 pm. The density of the element is ____________ g/cm3.
[NA = 6.0 × 1023 atom mol−1)
The percentage of unoccupied volume in simple cubic cell is ______.
The number of atoms in 500 g of a fcc crystal of a metal with density d = 10 g/cm3 and cell edge 100 pm, is equal to ____________.
An element crystallizes bcc type of unit cell, the density and edge length of unit cell is 4 g cm−3 and 500 pm respectively. What is the atomic mass of an element?
An element with density 2.8 g cm−3 forms fcc unit cell having edge length 4 × 10−8 cm. Calculate molar mass of the element.
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The number of atoms in 100 g of an fcc crystal with density 10 g cm-3 and unit cell edge length 200 pm is equal to ______.
The coordination number of atoms in body-centred cubic structure (bcc) is ______.
Gold crystallises into face-centred cubic cells. The edge length of a unit cell is 4.08 × 10–8 cm. Calculate the density of gold. [Molar mass of gold = 197 g mol–1]
An element has a bee structure with unit cell edge length of 288 pm. How many unit cells and number of atoms are present in 200 g of the element?
What is the density of potassium, if it has a bcc structure with edge length 4Å?
(Atomic mass of K = 39)
At room temperature, polonium Crystallises in a primitive cubic unit cell. If a = 3.36 Å. Calculate the theoretical density of polonium. [It's atomic weight is 209 g/mol.]
Silver crystallizes in the fcc structure. If the edge length of the unit cell is 400 pm, calculate the density of silver (Atomic mass of Ag = 108).
What is base centred (or end-centred) unit cell?
The total number of different primitive unit cells is ______.
What would be the empirical formula of a compound having a unit cell containing A ion shared equally at the corner of the cube and B ion on the centre of faces of the cube?
Which of the following metals exhibits minimum packing efficiency in its cubic system?
The cubic unit cell of a metal (molar mass = 63.55g mol−1) has an edge length of 362 pm. Its density is 8.92g cm−3.
The type of unit cell is ______.
Calculate the molar mass of an element having a density of 19.2 g cm−3 if it forms an fcc structure [a3 × NA = 40 cm3 mol−1].
