Concept explainers
Crystalline silicon has a cubic structure. The unit cell edge length is 543 pm. The density of the solid is 2.33 g/cm3. Calculate the number of Si atoms in one unit cell.
Interpretation:
The number of Silicon atoms in unit cell of Silicon cubic lattice has to be determined.
Concept introduction:
In crystalline solids, the components are packed in regular pattern and neatly stacked. The components are imagined as spheres and closely packed. This phenomenon is called “close packing” in crystals. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing.
Answer to Problem 11.43QP
The number of Silicon atoms in unit cell of Iron cubic lattice is
Explanation of Solution
Record the given data:
The unit cell is assumed that of a cubic shape and the edge length of the unit cell is given. Density of Silicon is given.
Calculate the volume of one unit cell of cubic lattice of Silicon.
Edge length of the cubic unit cell is given. The cubic value of edge length gives the volume of the unit cell.
Calculate the mass of one unit cell of cubic lattice of Silicon.
Density of the unit cell is given. The mass of unit cell is calculated using the equation
Calculate the average mass of one Silicon atom in unit cell.
The average mass of one Silicon atom in its crystal lattice is calculated using the atomic mass value of Silicon.
Calculate the number of Silicon atoms present in a unit cell.
The average mass of one Silicon atom in its crystal lattice is related to number of atoms per unit cell as follows –
Using this equation, the number of Silicon atoms present per unit cell has been calculated.
The number of Silicon atoms in unit cell of Silicon cubic lattice has been determined.
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Chapter 11 Solutions
Chemistry
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- Consider the three types of cubic units cells. (a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cubes edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is (4/3)r3, where r is the radius of the sphere.) (b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?arrow_forwardThe density of polonium metal is 9.2 g/cm3. If the extended lattice of polonium exhibits a simple cubic unit cell, estimate the atomic radius of polonium.arrow_forward
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