Finding the center of mass in a ammonia molecule...?

Question

In the ammonia (NH_3) molecule, the three hydrogen (H) atoms form an equilateral triangle; the center of the triangle is 9.40*10^-11 m from each hydrogen atom. The nitrogen (N) atom is the apex of a pyramid, with the three hydrogen atoms forming a base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is 10.14*10^-11 m. Locate the center of mass of the molecule relative to the nitrogen atom, and explain how you got your answer.

Answer 1

Hint: use trig to find the atomic coordinates. Apply the formula CM = SUM(RiMi)/SUM(Mi) where Ri is the position vector of atom i and Mi is the mass of atom i. Explain that you arrived at the answer through your own efforts.

Answer 2

The calculation is especially easy by using way the length are given. notwithstanding, it takes truly some history to get to the easy calculation. First, the middle of mass of a gadget of debris is defined as: Sum(mi * yi) / Sum(mi) the position mi are the a number of of the debris m1, m2,m3, and so on. and yi is the gap from the inspiration to the particle y1, y2, y3, and so on. The "Sum" notation ability to sum the relation over all debris. to locate the finished center of mass, you commonly opt to finish the above calculation in all 3 guidelines, x, y, and z. The calculation might want to be very much simplyfied at the same time as there is an axis or plane of symmetry because the middle of mass might want to lie on that axis or plane. you want to locate the middle of mass. because of symmetry, the middle of mass lies alongside the axis from the middle of the nitrogen to the middle of the hydrogen equilateral triangle. Set the inspiration on the nitrogen atom. you comprehend that the gap, alongside the axis, between the nitrogen and the hydrogen triangle is 0.037 nm and the finished mass of Hydrogen at that distance is 3 amu (mass of three hydrogens). because the nitrogen is on the inspiration, its distance is 0. Its mass is 14 amu. Sum(mi * yi) / Sum(mi) = (14 amu * 0 nm + 3 amu * 0.037 nm) / (14 amu + 3 amu) = 0.00653 amu using the formula from above: