An atom of rhodium (Rh) has a diameter of about 2.7×10−8 cm. a. What is the radius of a rhodium atom in angstroms (Å) and in meters (m)?

Verified step by step guidance

1. Convert the diameter of the rhodium atom from centimeters to meters by multiplying by $10^{-2}$, as there are 100 centimeters in a meter.
2. Calculate the radius in meters by dividing the diameter in meters by 2, since the radius is half the diameter.
3. Convert the radius from meters to angstroms by multiplying by $10^{10}$, because 1 meter equals $10^{10}$ angstroms.
4. Express the radius in scientific notation for clarity and to easily compare magnitudes in different units.
5. Verify units at each step to ensure consistency and correctness in the conversion process.

Key Concepts

Atomic Radius

The atomic radius is defined as the distance from the nucleus of an atom to the outer boundary of its surrounding cloud of electrons. It is typically measured in picometers (pm) or angstroms (Å), where 1 Å equals 10^-10 meters. Understanding atomic radius is crucial for determining the size of an atom and its interactions with other atoms.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this context, converting the diameter of the rhodium atom from centimeters to angstroms and meters requires knowledge of the relationships between these units. For example, 1 cm equals 10^8 Å and 1 cm equals 0.01 m, which are essential for accurate calculations.

Measurement of Atoms

Atoms are incredibly small, and their sizes are often expressed in terms of nanometers or angstroms. The measurement of atomic dimensions is typically done using techniques like X-ray diffraction or scanning tunneling microscopy. Recognizing the scale at which atoms exist helps in understanding their properties and behaviors in chemical reactions.