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What is the simplest formula of a solid containing a, b, and c atoms in a cubic lattice in which the a atoms occupy the corners, the b atoms the body-center position, and the c atoms the faces of the unit cell?


a. a4bc3


b. abc6


c. abc3


d. abc


e. a8bc6?

Respuesta :

znk

Answer:

c. abc₃  

Step-by-step explanation:

1. a atoms

There are eight corners, each containing an a atom.

No. of a atoms = 8 × ⅛

No. of a atoms = 1

=====

2. b atoms

There is one central b atom.

=====

3. c atoms

There are six faces, each containing a c atom.

No. of a atoms = 6 × ½

No. of c atoms = 3

=====

4. Formula

The simplest formula is abc₃.

Lanuel

The simplest formula of a solid containing a, b, and c atoms in a cubic lattice is: c. [tex]abc_3[/tex]

A unit cell can be defined as a repetitive unit of solid structures with equivalent edge points and opposite faces.

In crystal lattices, there are three (3) main types of unit cell and these include:

  • Body-centered cubic (BCC)
  • Face-centered cubic (FCC)
  • Simple cubic

A simple cubic unit cell is the simplest repetitive unit cell because the lattice points are only at the corners.

To calculate the simplest formula of a solid containing a, b, and c atoms in a cubic lattice:

For a atoms:

[tex]a = 8 \times \frac{1}{8}[/tex]

a = 1 atom

For b atoms:

[tex]b = 1 \times 1[/tex]

b = 1 atom

For c atoms:

[tex]c = 6 \times \frac{1}{2}[/tex]

c = 3 atoms

Simplest formula = [tex]abc_3[/tex]

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