Center of mass of NH3 molecule, not quite there

[1MileCrash]

Homework Statement

An amonia NH3 molecule in the figure has three hydrogen atoms, which form a equilateral triangle as the base of a pyramid. At the top of the pyramid is the nitrogen atom.

The length between any two hydrogen atoms is 9.4x10^-11, the length from nitrogen to any of the hydrogen atoms is 10.14x10^-11.

The mass ratio of nitrogen to hydrogen is 13.9.

The xaxis runs through the bottom of the pyramid, one of the points lies on it. The y-axis runs through the center of the pyramid vertically.

Homework Equations

The Attempt at a Solution

I am getting a close answer, but off enough to think I'm doing something wrong.

x center of mass is 0, by symmetry/intuition.

For y, what i did was try to find how high nitrogen is with the pythagorean theorem. I got that nitrogen should be at a height of 3.8x10^-11 along y axis.

I multiplied this number by 13.9, then divided by 16.9.


My result is 3.125x10^-11 for the ycom, but the correct answer is 3.08x10^-11. Why am I off by that amount?

 

[Doc Al]

For y, what i did was try to find how high nitrogen is with the pythagorean theorem. I got that nitrogen should be at a height of 3.8x10^-11 along y axis.

What triangle did you use?

 

[1MileCrash]

The reason for the error is that I took their word for it and just used 1 and 13.9, while they used the actual periodic table masses of N and H. 13.9 is pretty darn close to the actual ratio of mass between the two, but not close enough.

 

[Doc Al]

Good. Glad you figured it out.