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. There were \(1.12\times10^4\) iron atoms used in the image. b. The mass of the platinum atomic surface is approximately \(8.98 \times 10^{-21}\mathrm{g}\). c. \(5.42\times 10^2\) ruthenium atoms are needed to construct the surface with the same mass as the platinum surface.

Step-by-step solution

Find the number of iron atoms used

To find the number of iron atoms used, we need to divide the mass of the iron atoms by the atomic mass of iron. The atomic mass of iron is approximately 56 u (unified atomic mass units), where 1 u = 1.6605 × 10^-24 g. So, we have: Number of Iron atoms = (Total mass of iron atoms) / (Atomic mass of iron in grams) \( Number\, of\, Iron\, atoms=\frac{1.05\times 10^{-20}\, g}{(56\, u)\times(1.6605 \times 10^{-24} \mathrm{g/u})} \)

Calculate the number of iron atoms

Now we can calculate the number of iron atoms: \( Number\, of\, Iron\, atoms=\frac{1.05\times 10^{-20}\, g}{(56\, u)\times(1.6605 \times 10^{-24}\, g/u)}=1.12\times10^4\, atoms \) So, there were 1.12 x 10^4 iron atoms used.

Calculate the mass of the platinum surface

To find the mass of the atomic surface made of platinum, we first need to find the number of platinum atoms in the surface. Since it is 20 platinum atoms high and 14 platinum atoms wide, there are 20 x 14 = 280 platinum atoms. The atomic mass of platinum is about 195 u. Mass of the platinum surface = (Number of platinum atoms) x (Atomic mass of platinum in grams) \( Mass\, of\, the\, platinum\, surface=280\, atoms\, \times\, (195\, u)\times(1.6605 \times 10^{-24} \mathrm{g/u}) \)

Calculate the mass of the platinum surface

Now we can calculate the mass of the platinum surface: \( Mass\, of\, the\, platinum\, surface=280\, atoms\, \times\, (195\, u)\times(1.6605 \times 10^{-24}\, g/u)=8.9831\times10^{-21}\, g \) So, the mass of the platinum atomic surface is approximately 8.98 × 10^-21 g.

Find the number of ruthenium atoms needed

To find the number of ruthenium atoms needed, we need to divide the mass of the platinum surface by the atomic mass of ruthenium. The atomic mass of ruthenium is approximately 101 u. Number of ruthenium atoms = (Mass of platinum surface) / (Atomic mass of ruthenium in grams) \( Number\, of\, ruthenium\, atoms=\frac{8.9831\times 10^{-21}\, g}{(101\, u)\times(1.6605 \times 10^{-24} \mathrm{g/u})} \)

Calculate the number of ruthenium atoms

Now we can calculate the number of ruthenium atoms: \( Number\, of\, ruthenium\, atoms=\frac{8.9831\times 10^{-21}\, g}{(101\, u)\times(1.6605 \times 10^{-24}\, g/u)}=5.42\times 10^2\, atoms \) So, 5.42 x 10^2 ruthenium atoms are needed to construct the surface with the same mass as the platinum surface.

Key concepts

Scanning Tunneling Microscopy

Scanning tunneling microscopy (STM) is an innovative technique that allows scientists to visualize and manipulate individual atoms. It works by measuring the electric current that flows between a sharp metal tip and the surface being examined when they are brought very close together. STM is extremely powerful because it can image surfaces at the atomic level and even manipulate atoms to create atomic-scale structures.
This method has revolutionized fields such as nanotechnology and surface science, by enabling the creation of new materials with atomic precision.
STM offers the ability to "write" with atoms, arranging them in specific patterns or formations on a conductive surface, thus paving the way for unprecedented advancements in atomic data storage and quantum computing. STM's ability to see and move atoms one by one truly demonstrates the potential and future of atomic manipulation.

Atomic Mass

Atomic mass is a crucial property of atoms, representing the average mass of an atom relative to 1/12 the mass of carbon-12. It is measured in unified atomic mass units (u), which makes it easy to determine how many atoms are present in a particular mass.
For example, the atomic mass of iron is approximately 56 u, while that of platinum is around 195 u. This numerical value helps in calculating the quantity of atoms when their total mass is known, by dividing the mass by the atomic mass of the element.
This concept is fundamental when performing calculations in chemistry and physics, especially when dealing with reactions and the arrangement of atoms in compounds or solid structures. Atomic mass also helps in understanding isotopic distributions and the atomic weight of substances on Earth.

Iron Atoms

Iron atoms are fundamental components in numerous biological and geological processes. In the context of STM, iron atoms serve as markers or building blocks on atomic surfaces, allowing researchers to create visual representations at the nanoscale.
The atomic mass of iron is about 56 u, which is useful when calculating the number of iron atoms in a sample. By knowing the total mass and the atomic mass, scientists can determine the quantity of atoms involved. This principle was applied in our scenario where a total mass of iron atoms was used to create an image.
Iron is not only common in laboratories for experimental setups but also in the cores of planets, as it predominates in Earth's core and forms the basis for various minerals and ores mined globally.

Platinum Surface

Platinum surfaces serve as vital substrates in studies involving atomic manipulation due to their robust and stable characteristics. Platinum atoms are relatively large, with an atomic mass of approximately 195 u, making them ideal for precisely arranging other atoms to create images or patterns on their surface.
In our example, the platinum surface was organized 20 atoms high by 14 atoms wide, showing how atomic-level precision is critical in structure design. The total mass of such a surface can be calculated, helping scientists understand the atomic composition and behavior of complex networks on a nanoscale.
These platinum surfaces are utilized in various catalytic processes and play significant roles in chemical reactions due to their excellent conductive properties and chemical stability.

Ruthenium Atoms

Ruthenium atoms are used in atomic manipulation for their favorable properties and unique characteristics. With an atomic mass of about 101 u, ruthenium is lighter compared to platinum, but it still exhibits remarkable stability and conductivity.
In atomic scale experiments, ruthenium can serve as a substitute for other metals, bringing about similar physical properties without significantly altering the mass calculations. This ability is illustrated by the task of constructing a surface of similar mass to a platinum one using ruthenium atoms.
Ruthenium finds application in advanced technologies like electronics, catalysis, and even future computing, highlighting its versatility and importance in scientific research, especially when dealing with atomic and molecular structures.