Assume that the atomic diameter of an atom of element X is 2A and that 1.0 x 10(16th) atoms are arranged in a simple 2D square array. What is the length of each side in cm?
I would draw a 2D square. Each side is 1E8 atoms. If each atom is 2E-8 cm (that's 2 Angstroms each), then
1E8 atom x (2E-8 cm/atom) = ?
Is it 2E-11?
I don't think so. How do you add 8 and -8 and get -11.
To find the length of each side of the 2D square array, we need to determine the number of atoms that can fit in one row or column and then convert it into cm.
First, let's calculate the number of atoms in one row or column of the square array. Since the atoms are arranged in a square array, the total number of atoms is equal to the number of atoms per row multiplied by the number of rows.
Given that there are 1.0 x 10^16 atoms in the array, we can assume that the number of atoms per row (or column) is the square root of this total.
√(1.0 x 10^16) = 1.0 x 10^8 atoms
Now, to convert the atomic diameter from Angstroms (Å) to centimeters (cm), we need to know the conversion factor. 1 Å is equal to 1 x 10^(-8) cm. Therefore, the atomic diameter of element X (2Å) is equal to 2 x 10^(-8) cm.
Finally, to find the length of each side of the square array, we can multiply the number of atoms per row (or column) by the atomic diameter:
Length of each side = (Number of atoms per row) x (Atomic diameter)
Length of each side = (1.0 x 10^8 atoms) x (2 x 10^(-8) cm)
Length of each side = 2.0 cm
Hence, the length of each side of the square array is 2.0 cm.