I received the task to determine vectorially and explain how to obtain the angle of 109.5 degrees in the tetrahedral geometry? for covalent crystals.

Chemistry
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Chapter1: Chemical Foundations
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Good morning I am recently studying the topic of covalent crystals, I received the task to determine vectorially and explain how to obtain the angle of 109.5 degrees in the tetrahedral geometry? for covalent crystals.
Here I share a slide with the information and a small scheme.
Thank you very much in advance.

 

Covalent Crystals
The covalent bond is the classical electron pair or homopolar bond of
chemistry, particularly of organic chemistry. It is a strong bond: the bond be-
tween two carbon atoms in diamond with respect to separated neutral atoms is
comparable with the bond strength in ionic crystals.
The covalent bond has strong directional properties (Fig. 11). Thus car-
bon, silicon, and germanium have the diamond structure, with atoms joined to
four nearest neighbors at tetrahedral angles, even though this arrangement
gives a low filling of space, 0.34 of the available space, compared with 0.74 for a
close-packed structure. TheR tetrahedral bond allows only four nearest neigh-
bors, whereas a close-packéd structure has 12. We should not overemphasize
the similarity of the bonding of carbon and silicon. Carbon gives biology, but
silicon gives geology and semiconductor technology.
The covalent bond is usually formed from two electrons, one from each
atom participating in the bond. The electrons forming the bond tend to be
partly localized in the region between the two atoms joined by the bond. The
spins of the two electrons in the bond are antiparallel.
Tarea
-1-11 X
-11-1
(-1-1
Transcribed Image Text:Covalent Crystals The covalent bond is the classical electron pair or homopolar bond of chemistry, particularly of organic chemistry. It is a strong bond: the bond be- tween two carbon atoms in diamond with respect to separated neutral atoms is comparable with the bond strength in ionic crystals. The covalent bond has strong directional properties (Fig. 11). Thus car- bon, silicon, and germanium have the diamond structure, with atoms joined to four nearest neighbors at tetrahedral angles, even though this arrangement gives a low filling of space, 0.34 of the available space, compared with 0.74 for a close-packed structure. TheR tetrahedral bond allows only four nearest neigh- bors, whereas a close-packéd structure has 12. We should not overemphasize the similarity of the bonding of carbon and silicon. Carbon gives biology, but silicon gives geology and semiconductor technology. The covalent bond is usually formed from two electrons, one from each atom participating in the bond. The electrons forming the bond tend to be partly localized in the region between the two atoms joined by the bond. The spins of the two electrons in the bond are antiparallel. Tarea -1-11 X -11-1 (-1-1
Expert Solution
Step 1

If we put the atom in the four alternate corner of a cube then a tetrahedral structure is formed.

The atoms position are denoted by A,B,C and D and O is the central point whose position coordinate is (0,0,0)

So the position coordinate of A =(1,-1,1)

the position coordinate of B = (1,1,-1)

the position coordinate of C = (-1,1,1)

the position coordinate of B = (1,1,-1)

OA represented by vector 'a'

OB represented by vector 'b'

And let the angle between them is θ.

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