The diameter of a helium atom is about \(1 \times 10^{2} \mathrm{pm}\). Suppose that we could line up helium atoms side by side in contact with one another. Approximately how many atoms would it take to make the distance from end to end \(1 \mathrm{~cm} ?\)

Understanding the size of a helium atom is crucial when delving into the microscopic world. So, just how small is a helium atom? It has a diameter of approximately 100 picometers (pm), which is a unit of length in the metric system that's used to measure atomic and molecular scales. To visualize this, if you lined up 10 million helium atoms, they would barely stretch to a millimeter! These dimensions give us an insight into the atomic model and the relative size of particles that make up the universe.

The concept of atomic size also lays the foundation for understanding chemical bonding and material properties, as atom size affects how atoms interact with one another. In the context of the given problem, knowing that each helium atom is about 100 pm in diameter is the starting point for determining how many atoms it would take to cover a given distance.

When working within the realm of physics and chemistry, the ability to convert units is an essential skill. This conversion enables us to compare and calculate different magnitudes and measurements seamlessly. For instance, in our exercise, we encounter picometers (pm) and centimeters (cm), which are vastly different scales.

Conversions follow a basic rule where you multiply or divide by factors of 10. Knowing the conversion factor between picometers and centimeters—that is, 1 cm equals 10 billion picometers (\(1 \times 10^{10}\text{pm}\))—is key to solving our task. Mastering unit conversions is not just a trivial math skill, it's a bridge that connects various scientific concepts and real-world applications.

Comparing sizes that span a broad range, from picometers to centimeters, can seem daunting. But, it's just a matter of scale. There are one trillion picometers in one meter. Therefore, since 1 centimeter is one-hundredth of a meter, a centimeter consists of 10 billion picometers (\( 1 \times 10^{10}\text{pm}\)).

To convert picometers to centimeters, you divide the number of picometers by 10 billion. This method is utilized in the problem to determine how many of the tiny helium atoms, measured in picometers, fit across a length measured in centimeters. It's a fascinating exercise in understanding the vast differences in scales that we deal with in science.

In science, dealing with extremely large or small numbers is common, and that's where scientific notation comes into play, providing a method to express such numbers concisely. Scientific notation represents numbers as a product of a decimal number between 1 and 10 multiplied by a power of 10. For example, the number 100 is expressed as \(1 \times 10^{2}\) and the number 10 billion as \(1 \times 10^{10}\).

This notation simplifies calculations and communication of measurements with a high degree of precision, like atomic dimensions. As seen in the given problem, we use scientific notation to conveniently describe the size of a helium atom and the length in picometers, and to compute how many atoms can fit into a centimeter.