If a crystal lattice has 6 closed-pack spheres, what the number of tetrahedral voids in the lattice?a)12b)6c)36d)3Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Explanation:
A closed-pack structure has tetrahedral voids and octahedral voids. A tetrahedral void is the space between four spheres forming a tetrahedron, while an octahedral void is the space between six spheres forming an octahedron.

Given that the crystal lattice has 6 closed-pack spheres, it means that there are 6 octahedral voids in the lattice. However, we need to determine the number of tetrahedral voids in the lattice.

To do this, we can use the formula:

Number of tetrahedral voids = 2 × Number of atoms in the lattice

Since a closed-pack structure has 4 atoms, we have:

Number of tetrahedral voids = 2 × 4 = 8

However, each tetrahedral void is shared by two closed-pack structures. Therefore, we have:

Number of tetrahedral voids = 8 ÷ 2 = 4

Therefore, the number of tetrahedral voids in the lattice is 4. However, since the question asks for the number of tetrahedral voids per closed-pack structure, we need to divide 4 by 2 (the number of closed-pack structures). Hence, we have:

Number of tetrahedral voids per closed-pack structure = 4 ÷ 2 = 2

Therefore, the correct answer is option A, which states that there are 12 tetrahedral voids in the lattice.

Answer

For a crystal lattice, if there are N close-packed spheres the number of tetrahedral voids are 2N and number octahedral voids are N. For N=6, number of tetrahedral voids = 2 × 6 = 12.

Similar Class 12 Doubts

Which of the following is a correct statement ?

a solid A+ and B- has NaCl type closed packed structure. if the anion has radius of 241.5 . what should be the ideal radius of cation? can a C+ having radius of 50 pm be fitted into tetrahedral holes of the crystal A+B- ?

A compound forms hexagonal closed packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?

How will you distinguish between the following pairs of terms: (i) Hexagonal close-packing and cubic close-packing? (ii) Crystal lattice and unit cell? (iii) Tetrahedral void and octahedral void?

If a is the edge length of the unit cell of an atomic crystal having fcc lattice then what is the distance of closest approach between the two atoms in the crystal?

Top Courses for Class 12

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams