Question

In a methane (CH2) molecule each hydrogen atom is at a corner of a regular tetrahedron with the
carbon atom at the centre. In coordinates where one of the C-H bonds is in the direction of i cap+j cap+k cap
an adjacent C-H bond in the î-jcap -k cap direction. Then angle between these two bonds :-​

Answer 1

In a methane (CH2) molecule each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the centre. In coordinates where one of the C-H bonds is in the direction of (i + j + k)

an adjacent C-H bond in the (i - j - k) direction.

then we have find angle between these two bonds.

we know, if two vectors A and B are given then, angle between them, α = cos^-1(A.B/|A||B|)

let A = (i + j + k) and B = (i - j - k)

A.B = (i + j + k).(i - j - k) = 1 - 1 - 1 = -1

|A| = √(1² + 1² + 1²) = √3

|B| = √{1² + (-1)² + (-1)²} = √3

so, angle between them, α = cos^-1(-1/√3.√3) = cos^-1(-1/3) ≈ 109.5°

hence,angle between given bonds is 109.5°