Question

What is the approximate size (in \(\mathrm{cm}\) ) of an atom?

Short answer

The approximate size of an atom is about \(1.0 \times 10^{-8} \text{ cm}\).

Step-by-step solution

Understanding Atomic Size

Atoms are the basic building blocks of matter and are extremely small. When measuring the size of an atom, we refer to its atomic radius, which is typically given in picometers or angstroms.

Define Unit Conversion

To convert the atomic radius from picometers to centimeters, remember that 1 picometer ( ext{pm}) is equal to 1 imes 10^{-12} meters (m). Since 1 centimeter (cm) is equal to 1 imes 10^{-2} meters, you can convert the size into centimeters by using these conversions.

Atomic Size Range

Most atoms have radii in the range of about 30 pm to 300 pm. For simplification, let's take an average medium-sized atom with a radius of approximately 100 pm.

Calculate Size in Centimeters

Convert 100 pm to meters: \(100 \times 10^{-12} \text{ m}\). Now convert this into centimeters: \(100 \times 10^{-12} \text{ m} = 100 \times 10^{-12} \times 10^{-2} \text{ cm} = 1.0 \times 10^{-8} \text{ cm} \).

Key concepts

Understanding Unit Conversion

Unit conversion is a fundamental concept used in various scientific calculations, including chemistry and physics. It allows you to switch from one measurement unit to another, ensuring consistency and accuracy in calculations.
To perform a unit conversion, you often use a conversion factor. This factor is a fraction that equals one, aside from its units. For instance, in converting lengths from meters to centimeters, where 1 meter equals 100 centimeters, the conversion factor would be 1 meter/100 centimeters. Remember, the value of the quantity doesn't change; only its units do, which makes this method powerful and reliable for scientific computations.
Being adept at unit conversions enables you to solve problems that require consistent units, making it easier to communicate your results effectively in scientific contexts.

Exploring Atomic Measurement

Atoms are so small that measuring them requires a different approach compared to measuring macroscopic objects. One way to describe an atom's size is through its atomic radius. The atomic radius is the distance from the center of an atom's nucleus to its outermost electron.
Atomic measurements typically use very tiny units, such as picometers (pm) or angstroms (8A). These units are chosen because they align well with the size of atoms, providing a scale that's comprehensible when expressed in these smaller units.
Understanding atomic measurement is crucial for studying elements and compounds because knowing the size and structure of atoms can affect their chemical properties and interactions. It gives insight into the fundamental aspects of matter and enhances our understanding of the physical world.

Converting Picometers to Centimeters

Converting picometers to centimeters involves two main steps due to the large difference in the size of these units. One picometer (9pm) is incredibly small: it's equivalent to \(1 \times 10^{-12}\) meters. In contrast, a centimeter (cm) is \(1 \times 10^{-2}\) meters.

• **Step 1:** Convert picometers to meters. If you have an atom with a radius of 100 pm, you multiply: \(100 \times 10^{-12} \text{ m}\).
• **Step 2:** Convert meters to centimeters by applying the conversion factor from meters to centimeters: \(100 \times 10^{-12} \times 10^{-2} \text{ cm}\), which results in \(1.0 \times 10^{-8} \text{ cm}\).

By understanding and applying these steps, you can accurately convert between these units, which is essential when dealing with scientific data that requires precise measurements. It bridges the gap between the scale at which atomic properties are measured and more tangible units of length, like centimeters.