Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's say I have a molecular like CH3F (i.e. fluoromethane), and I'm able to measure the angle (theta) between the C-H bonds. Provided (theta) what is the angle between the C-F bond and the C-H bonds?

share|cite|improve this question
up vote 2 down vote accepted

Use a coordinate system with the C at the origin and the F on the $z$ axis, and one of the H's in the $xz$ plane. Let $\alpha$ be the angle between the C-F and C-H bonds and $\theta$ be the angle between two C-H bonds. The Cartesian components of unit vectors in the directions of the 3 H's are $$ (\sin\alpha,0,\cos\alpha),(\sin\alpha\cos 2\pi/3,\sin\alpha\sin 2\pi/3,\cos\alpha),(\sin\alpha\cos 4\pi/3,\sin\alpha\sin 4\pi/3,\cos\alpha). $$ The dot product of any two of these should equal $\cos\theta$: $$ \cos\theta=\sin^2\alpha\cos 2\pi/3+\cos^2\alpha=-{1\over 2}\sin^2\alpha+\cos^2\alpha={3\over 2}\cos^2\alpha-{1\over 2}. $$ The solution is $$ \cos\alpha=\pm\sqrt{1+2\cos\theta\over 3}. $$ The negative root is the relevant one here, since we know $\alpha$ is obtuse.

If you happen to remember that the angle for methane is $\theta=\cos^{-1}(-1/3)$, you can check that this makes sense: the above formula gives $\alpha=\theta$ in that case, as it should.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.