Question

The closest packing of spheres (such as oranges, cannonballs, or atoms) has the spheres ________

arranged in a square pattern with a sphere at each corner of the square.

arranged in layers with each sphere surrounded by 3 other spheres in the layer.

arranged in layers with each sphere surrounded by 4 other spheres in the layer.

arranged in layers with each sphere surrounded by 6 other spheres in the layer.

arranged in a square pattern with a sphere at each corner and one in the center of the square.

Answer 1

When a single layer of spheres is arranged into the shape of a hexagon, gaps are left uncovered. The hole formed between three spheres is called a trigonal hole because it resembles a triangle. In the example below, two out of the the six trigonal holes have been highlighted green.

Once the first layer of spheres is laid down, a second layer may be placed on top of it. The second layer of spheres may be placed to cover the trigonal holes from the first layer. Holes now exist between the first layer (the orange spheres) and the second (the lime spheres), but this time the holes are different. The triangular-shaped hole created over a orange sphere from the first layer is known as a tetrahedral hole. A hole from the second layer that also falls directly over a hole in the first layer is called an octahedral hole.

Answer-> arranged in layers with each sphere surrounded by 6 other spheres in the layer