Question

With the advent of techniques such as scanning tunneling microscopy, it is now possible to "write" with individual atoms by manipulating and arranging atoms on an atomic surface. a. If an image is prepared by manipulating iron atoms and their total mass is \(1.05 \times 10^{-20} \mathrm{g},\) what number of iron atoms were used? b. If the image is prepared on a platinum surface that is exactly 20 platinum atoms high and 14 platinum atoms wide, what is the mass (grams) of the atomic surface? c. If the atomic surface were changed to ruthenium atoms and the same surface mass as determined in part b is used, what number of ruthenium atoms is needed to construct the surface?

Short answer

a. The number of iron atoms used in the image is approximately \(1.13 \times 10^3\) atoms. b. The mass of the platinum surface is approximately \(8.64 \times 10^{-20}\) grams. c. The number of ruthenium atoms needed to construct the surface is approximately \(514\) atoms.

Step-by-step solution

Calculate the number of iron atoms used in the image

To find the number of iron atoms used in the image, we will use the given mass and the atomic mass of iron. First, we need to know the atomic mass of Iron which is 55.845 amu (atomic mass units). We also need to recall that 1 mole of any element has a mass (grams) equal to its atomic mass in amu, and that 1 mole contains Avogadro's number of atoms (\(6.022 \times 10^{23}\) atoms). In this case, we have mass = \(1.05 \times 10^{-20}\) grams. Now we'll calculate the number of moles of iron atoms in the given mass: Number of moles = \(\frac{mass}{molar\,mass}\) Then, we'll multiply the number of moles by Avogadro's number to obtain the number of atoms present.

Calculate the mass of the platinum surface

To find the mass of the platinum surface, given dimensions in terms of atoms, we will use the atomic mass of platinum and the number of atoms of platinum. We are given that the surface is 20 atoms high and 14 atoms wide, so the total number of atoms is their product: Total atoms = 20 atoms × 14 atoms = 280 atoms The atomic mass of platinum is 195.084 amu. Using the same concept as in Step 1, we will convert this into moles, then into mass (grams).

Calculate the number of ruthenium atoms needed to construct the surface

To find the number of ruthenium atoms needed, given the same surface mass calculated in Step 2, we will first calculate the number of moles and then the number of atoms. The atomic mass of ruthenium is 101.07 amu. We will first calculate the number of moles of ruthenium using the surface mass from Step 2, then multiply it by Avogadro's number to find the number of ruthenium atoms needed. Now we have all the information to answer parts a, b, and c of the exercise.