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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.
An element with molar mass 27 g/mol forms a cubic unit cell with edge length of 405 p.m. If the density of the element is 2.7 g/cm3, what is the nature of the cubic unit cell?
Give the percentage of empty space in bcc lattice.
Calculate the number of unit cells in 0.3 g of a species having density of 8.5 g/cm3 and unit cell edge length 3.25 × 10-8 cm.
What is the percentage of unoccupied space in fcc unit cell?
How many total constituent particles are present in simple cubic unit cell?
The percentage of unoccupied volume in simple cubic cell is ______.
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If the edge of a body-centred unit cell is 360 pm, what will be the approximate radius of the atom present in it? (in pm)
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?
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A metallic element has a cubic lattice with edge length of unit cell 2 Å. Calculate the number of unit cells in 200 g of the metal, if density of metal is 2.5 g cm-3?
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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?
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What is base centred (or end-centred) unit cell?
The total number of different primitive unit cells is ______.
An element crystallises in fee structure. If molar mass of element is 72.7 g mol -1, the mass of its one unit cell will be ______.
The number of particles present in Face Centred Cubic Unit cell is/are ______.
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.
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