Question

Why the tetrahedron is equal to the angle of 109.5degrees but it says in an article that if you divide the number of bonds thats the angle but when i divide 4 to 360 the answer is 90 they did not match pls answer my question tnx?

Answer 1

A tetrahedron is not flat...

Explanation:

If you have a flat symmetrical molecule such as Borane `BH_3` then dividing `360^@` by the number of bonds makes sense, but in the case of a three dimensional tetrahedral molecule such as Methane `CH_4` it does not.

You could model the shape by imagining a carbon atom at `(0, 0, 0)` and hydrogen atoms at: `(1, 1, 1)`, `(1, -1, -1)`, `(-1, 1, -1)` and `(-1, -1, 1)` (alternate vertices of a cube form the vertices of a tetrahedron).

Then the angle between the line joining `(0, 0, 0)` and `(1, 1, 1)` and the line joining `(0, 0, 0)` and `(1, -1, -1)` is:

`arccos((<1,1,1> . <1,-1,-1>)/(abs(<1,1,1>)*abs(<1,-1,-1>))) = arccos(-1/3) ~~ 109.5^@`