Question

In the ammonia (NH3) molecule of the figure, three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 × 10x^–11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is L = 10.14 × 1x^0–11 m. What are the (a) x and (b) y coordinates of the molecule's center of mass?

Answer 1

The centre of mass of the molecule will lie along the line joining the centre of the equilateral triangle to the Nitrogen atom.

Lets suppose that the centre of the equilateral triangle is at the origin (0,0). So we know that the x-cordinate of the centre of mass is zero.

Now, let the distance of Nitrogen atom from the origin be

using the pythagorean theorem -

mass of Hydrogen atom and mass of Nitrogen atom are in the ratio-

Centre of mass of the three hydrogen atoms in the equilateral tiangle is at the origin due to symmetry, therefore both x- and y-cordinates of center of mass of the three hydrogen atoms are zeroes.

Now, y -cordinate of the centre of mass of the entire ammonia molecule is,

is the distance of center of mass from the origin

Distance of center of mass from the nItrogen atom is