The diameter of a rubidium atom is 495 pm We will consider two different ways of placing the atoms on a surface. In arrangement A, all the atoms are lined up with one another to form a square grid. Arrangement B is called a close-packed arrangement because the atoms sit in the 'depressions' formed by the previous row of atoms: (a) Using arrangement A, how many Rb atoms could be placed on a square surface that is 1.0 cm on a side?

Verified step by step guidance

1. Convert the diameter of a rubidium atom from picometers to centimeters. Remember that 1 pm = 1 x 10^{-12} m and 1 m = 100 cm.
2. Calculate the area occupied by one rubidium atom in arrangement A. Since the atoms form a square grid, the area occupied by one atom is the square of its diameter.
3. Determine the area of the square surface, which is given as 1.0 cm on each side.
4. Divide the area of the square surface by the area occupied by one rubidium atom to find the number of atoms that can fit on the surface.
5. Ensure that the units are consistent throughout the calculation to avoid any errors.

Key Concepts

Atomic Diameter and Unit Conversion

The atomic diameter of rubidium is given as 495 picometers (pm), which is a unit of length equal to 10^-12 meters. To solve the problem, it's essential to convert the dimensions of the surface from centimeters to picometers, as 1 cm equals 10^10 pm. This conversion allows for consistent units when calculating how many atoms can fit on the surface.

Surface Area Calculation

The surface area of a square is calculated using the formula A = side^2. In this case, the side length of the square surface is 1.0 cm, which must be converted to picometers before applying the formula. Understanding how to calculate the area is crucial for determining how many rubidium atoms can be arranged on the surface.

Arrangement of Atoms

In arrangement A, the rubidium atoms are aligned in a square grid, meaning each atom occupies a specific area based on its diameter. To find the total number of atoms that can fit, divide the total surface area by the area occupied by one atom. This concept is fundamental in understanding how atomic arrangements affect packing efficiency on a surface.