An atom of rhodium (Rh) has a diameter of about 2.7×10−8 cm. c. If you assume that the Rh atom is a sphere, what is the volume in m3 of a single atom?

검증된 단계별 안내

Convert the diameter of the Rhodium atom from centimeters to meters by multiplying by \(10^{-2}\), since there are 100 centimeters in a meter.

Calculate the radius of the Rhodium atom by dividing the diameter by 2.

Use the formula for the volume of a sphere, which is \(V = \frac{4}{3} \pi r^3\), where \(r\) is the radius of the sphere.

Substitute the radius value obtained in step 2 into the volume formula.

Ensure the final volume is expressed in cubic meters (m^3).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Volume of a Sphere

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. To find the volume of a rhodium atom, one must first convert the diameter into radius by dividing it by two. This formula is essential for determining the space occupied by the atom when modeled as a sphere.

Unit Conversion

In chemistry, it is often necessary to convert units to ensure consistency, especially when dealing with measurements in different systems. In this case, the diameter of the rhodium atom is given in centimeters, but the final volume needs to be expressed in cubic meters (m³). Understanding how to convert between these units is crucial for accurate calculations.

Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in a compact form, using powers of ten. For example, 2.7×10−8 cm represents a very small measurement. Familiarity with scientific notation is important in chemistry for handling measurements and calculations involving atomic and molecular scales.