Answer
Verified
384.6k+ views
Hint: In order to solve this problem, we must firstly understand the type of unit cell present in the structure of NaCl. Then we can calculate the total number of atoms present in this unit cell and by relation, correspond the value of the total number of atoms to NaCl.
Complete step by step answer:
NaCl is an ionic crystalline compound. While formation of the crystal structure of sodium chloride, it crystallizes into a packing structure known as face – centred cubic. This packing structure forms a single unit in the multi – molecule lattice structure of sodium chloride. In this type of unit – cell, i.e. face centred cubic, the following characteristics are observed:
In face centred cubic structure, there are atoms on all the vertices of the cube
Atoms are also present on all the sides of the cube
The vertices have $\dfrac{1}{8}$ th of an atom on every vertex due to geometric constraints
Similarly, all faces have only \[\dfrac{1}{2}\] of an atom on every face due to geometric constraints
From this, we can infer that there are 8 portions of the $\dfrac{1}{8}$ th of an atom on the 8 vertices of the cube, while all the 6 sides of the cube have ½ atoms each. Hence the total number of atoms present in the face centred cubic structure can be calculated to be:
Total number of atoms = $\dfrac{1}{8}$ (8 vertices) + \[\dfrac{1}{2}\] (6 faces) = 1 + 3 = 4 atoms
Hence, there are 4 atoms present in each unit cell of a face centred cubic structure.
Hence, the number of NaCl units present in a unit cell of NaCl is 4
Hence, Option C is the correct option.
Note:
NaCl has a cubic unit cell that can be represented as a face-centred cubic array of anions with an interpenetrating fcc cation lattice (or vice-versa). This unit cell of NaCl looks the same whether we start with cations or anions at the corners. Each of these ions is 6-coordinate and has a local octahedral geometry.
Complete step by step answer:
NaCl is an ionic crystalline compound. While formation of the crystal structure of sodium chloride, it crystallizes into a packing structure known as face – centred cubic. This packing structure forms a single unit in the multi – molecule lattice structure of sodium chloride. In this type of unit – cell, i.e. face centred cubic, the following characteristics are observed:
In face centred cubic structure, there are atoms on all the vertices of the cube
Atoms are also present on all the sides of the cube
The vertices have $\dfrac{1}{8}$ th of an atom on every vertex due to geometric constraints
Similarly, all faces have only \[\dfrac{1}{2}\] of an atom on every face due to geometric constraints
From this, we can infer that there are 8 portions of the $\dfrac{1}{8}$ th of an atom on the 8 vertices of the cube, while all the 6 sides of the cube have ½ atoms each. Hence the total number of atoms present in the face centred cubic structure can be calculated to be:
Total number of atoms = $\dfrac{1}{8}$ (8 vertices) + \[\dfrac{1}{2}\] (6 faces) = 1 + 3 = 4 atoms
Hence, there are 4 atoms present in each unit cell of a face centred cubic structure.
Hence, the number of NaCl units present in a unit cell of NaCl is 4
Hence, Option C is the correct option.
Note:
NaCl has a cubic unit cell that can be represented as a face-centred cubic array of anions with an interpenetrating fcc cation lattice (or vice-versa). This unit cell of NaCl looks the same whether we start with cations or anions at the corners. Each of these ions is 6-coordinate and has a local octahedral geometry.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE