How many unit cells are present in the cube shaped ideal crystal of $\text{NaCl}$ mass $1.00$ gm?
Answer
635.4k+ views
Hint: The unit cell of a crystal structure can be defined as the building block of a crystal structure which on repetition in the three dimensions would result in the formation of the crystal lattice.
Complete step by step answer:
The crystal lattice exists in different unit cells such as, the primitive unit cell, the body-centred unit cell, the face-centred unit cell, and the end-centred unit cells.
So for the face centred one, as there are 6 atoms on each face of the unit cell that is shared by two other unit cells, we get 3 atoms from there and 1 atom from the corners which makes a total of 4 atoms in the face-centred cubic cell.
Now, the molecular mass of $\text{NaCl}$ = $23+35.5$= $58.5$ grams = $6.023\times {{10}^{23}}$ molecules of sodium chloride.
Therefore, 1 gram of $\text{NaCl}$ = $\dfrac{6.023}{58.5}\times {{10}^{23}}$ molecules = $1.02\times {{10}^{22}}$ molecules of sodium chloride.
Now, as each unit cell of a face-centred cubic unit cell contains 4 molecules of sodium chloride, therefore the number of unit cells present in $1.00$ gm of sodium chloride
= $\dfrac{1.02\times {{10}^{22}}}{4}$ = $2.57\times {{10}^{21}}$ unit cells of sodium chloride.
Note:
Each unit cell contains a certain number of constituent particles. For example, in the primitive unit the corners of each cell is shared by eight different atoms and hence each corner gets $\dfrac{1}{8}$ of the atom. As there are 8 corners so the total unit cell gets 1 atom in total.
Complete step by step answer:
The crystal lattice exists in different unit cells such as, the primitive unit cell, the body-centred unit cell, the face-centred unit cell, and the end-centred unit cells.
So for the face centred one, as there are 6 atoms on each face of the unit cell that is shared by two other unit cells, we get 3 atoms from there and 1 atom from the corners which makes a total of 4 atoms in the face-centred cubic cell.
Now, the molecular mass of $\text{NaCl}$ = $23+35.5$= $58.5$ grams = $6.023\times {{10}^{23}}$ molecules of sodium chloride.
Therefore, 1 gram of $\text{NaCl}$ = $\dfrac{6.023}{58.5}\times {{10}^{23}}$ molecules = $1.02\times {{10}^{22}}$ molecules of sodium chloride.
Now, as each unit cell of a face-centred cubic unit cell contains 4 molecules of sodium chloride, therefore the number of unit cells present in $1.00$ gm of sodium chloride
= $\dfrac{1.02\times {{10}^{22}}}{4}$ = $2.57\times {{10}^{21}}$ unit cells of sodium chloride.
Note:
Each unit cell contains a certain number of constituent particles. For example, in the primitive unit the corners of each cell is shared by eight different atoms and hence each corner gets $\dfrac{1}{8}$ of the atom. As there are 8 corners so the total unit cell gets 1 atom in total.
Recently Updated Pages
Which of the following graphs shows the variation of class 12 physics CBSE

Draw a labelled diagram of the human male reproductive class 12 biology CBSE

Describe the experiment to compare the emf of two cells class 12 physics CBSE

What is standard hydrogen electrode

What is conventional current and electric current class 12 physics CBSE

2Bromopentane is treated with an alcoholic KOH solution class 12 chemistry CBSE

Trending doubts
Draw a labelled sketch of the human eye class 12 physics CBSE

Which are the Top 10 Largest Countries of the World?

A member of Simon commission later became Prime Minister class 12 social science CBSE

Draw ray diagrams each showing i myopic eye and ii class 12 physics CBSE

Give one example of a reptile that is viviparous class 12 biology CBSE

Which is the correct genotypic ratio of mendel dihybrid class 12 biology CBSE

