Answer
Verified
429.3k+ views
Hint: We know that any crystal lattice is made up of very large unit cells and every lattice point is occupied by one constituent particle (atom, molecular, or ion). We must consider three types of cubic unit cells and for simplicity assume that the constituent particle is an atom, which is a primitive cubic unit cell, body-centered cubic unit cell, and face-centered cubic unit cell.
Complete step by step solution:
A Body-centred cubic (bcc) unit cell with an atom at each of its corners and also one atom at its body center. An atom at the body center can be seen that wholly belongs to the unit cell in which it is present.
Hence, in a bcc unit cell:
(i) $8~corners\times \dfrac{1}{8}per~~corner~atom=8\times \dfrac{1}{8}$ = 1 atom
(ii) 1 body centre atom = $1\times 1$ = 1 atom
Therefore, total number of atoms per unit cell for bcc, Z = 2 atoms
Given, edge of lattice (a) = $3\times {{10}^{-8}}cm$
Density of element (d) = $6.89gc{{m}^{-3}}$
${{N}_{A}}=6.022\times {{10}^{23}}mo{{l}^{-1}}$
Molar mass of element (M) = $\dfrac{d\times {{N}_{A}}\times {{a}^{3}}}{Z}$
M = $\dfrac{6.89\times 6.022\times {{10}^{23}}\times {{(3\times {{10}^{-8}})}^{3}}}{2}=56.013g\simeq 56g$
Hence, the molar mass of the element is 56g
Note: A cubic crystal is made up of a crystal lattice or a space lattice structure. A repeating arrangement of a space lattice is made up of unit cells. The most basic structure of a crystalline solid is a unit cell. The density of the unit cell is said to be the density of the cubic crystal itself.
Complete step by step solution:
A Body-centred cubic (bcc) unit cell with an atom at each of its corners and also one atom at its body center. An atom at the body center can be seen that wholly belongs to the unit cell in which it is present.
Hence, in a bcc unit cell:
(i) $8~corners\times \dfrac{1}{8}per~~corner~atom=8\times \dfrac{1}{8}$ = 1 atom
(ii) 1 body centre atom = $1\times 1$ = 1 atom
Therefore, total number of atoms per unit cell for bcc, Z = 2 atoms
Given, edge of lattice (a) = $3\times {{10}^{-8}}cm$
Density of element (d) = $6.89gc{{m}^{-3}}$
${{N}_{A}}=6.022\times {{10}^{23}}mo{{l}^{-1}}$
Molar mass of element (M) = $\dfrac{d\times {{N}_{A}}\times {{a}^{3}}}{Z}$
M = $\dfrac{6.89\times 6.022\times {{10}^{23}}\times {{(3\times {{10}^{-8}})}^{3}}}{2}=56.013g\simeq 56g$
Hence, the molar mass of the element is 56g
Note: A cubic crystal is made up of a crystal lattice or a space lattice structure. A repeating arrangement of a space lattice is made up of unit cells. The most basic structure of a crystalline solid is a unit cell. The density of the unit cell is said to be the density of the cubic crystal itself.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE