Geometry of Methane: Finding the Distance Between Hydrogen and Carbon Atoms

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Homework Help Overview

The discussion revolves around determining the distance between hydrogen and carbon atoms in a methane molecule, specifically in relation to the geometry of a cube where hydrogen atoms are positioned at its corners. The problem involves applying the Pythagorean theorem to find the length of the hypotenuse in a right triangle formed by these atoms.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the Pythagorean theorem to find distances within the cube. There are attempts to clarify the relationships between the sides of the triangle formed by the atoms, with specific focus on identifying the lengths of AP and OP. Questions arise about how to express the hypotenuse AO in terms of the edge length e of the cube.

Discussion Status

The discussion is active, with participants exploring different interpretations of the triangle's geometry. Some guidance has been provided regarding the identification of triangle sides, and there is a recognition of the relationship between the distances involved. However, there is no explicit consensus on the methods used to derive the final expressions.

Contextual Notes

Participants are working with a specific geometric configuration and are constrained by the information provided in the problem statement. There is an emphasis on understanding the relationships between the distances without having all the necessary details explicitly outlined.

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Homework Statement



In a methane molecule, determine the length of the distance between a hydrogen atom at A and the carbon atom at O (see diagram) in terms of the length of the edge (e) of the cube at four of whose corners the hydrogen atoms rest.

Screen Shot 2016-04-06 at 10.22.09 AM.png


Homework Equations



pythagorean theorem?

3. The Attempt at a Solution


The first part of the problem asks to find AB (see diagram). AB= e(sqrt-2).

The book gives the answer as AO=e(sqrt-3)/2, but I don't know how they got it.

I'm sure this is simple! I'm just not having any luck.

Thanks!
 
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Hi crastinus, you can UPLOAD your file and attach it to your post. Then you can insert it in the text where you want it. Use the UPLOAD button in the lower right corner of the edit pane.
 
Ah. I see it now. Thanks! Edits made.
 
From your image:
upload_2016-4-6_10-22-57.png


Note the plane image of the triangle in question. APO is a right triangle with AO as its hypotenuse. Can you find values for AP and OP?
 
If I'm right that AB= e(sqrt2), then AP=e(sqrt2)/2.

How to find AO? If I knew that this were a certain type of triangle, 45-45 or 30-60, I could determine AO. So, my question is: How can I determine AO knowing only one side and the right angle of triangle AOP. I know the various angles involved, but the point is to get AO in terms of e. That's what I'm not sure how to do.

Thanks!
 
You should be able to determine OP. Where is O located in the cube? Where is P located?
 
Wow. OK. Yes. OP=e/2.

And so, A0=(e/2)^2 + (e(sqrt2)/2)^2, which gives us AO=(e(sqrt3)/2)!

Thanks. Sometimes I just don't see what I'm looking at.
 

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