What is the density of lithium metal in g/cm3 if a cylindrical wire with a diameter of 2.40 mm and a length of 15.0 cm has a mass of 0.3624 g?

검증된 단계별 안내

First, we need to calculate the volume of the cylindrical wire. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. In this case, the diameter is given, so the radius would be half of the diameter.

Next, convert the diameter from millimeters to centimeters, since the density is asked in g/cm³. Remember that 1 cm = 10 mm.

Then, substitute the radius and the length (height) into the volume formula and calculate the volume of the lithium wire.

After that, use the formula for density, which is density = mass/volume. The mass of the lithium wire is given in the problem.

Finally, substitute the mass and the calculated volume into the density formula to find the density of the lithium metal.

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주요 개념

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

Density

Density is defined as the mass of an object divided by its volume, typically expressed in grams per cubic centimeter (g/cm³). It is a physical property that helps identify substances and can be calculated using the formula: density = mass/volume. Understanding density is crucial for solving problems related to the physical characteristics of materials.

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length) of the cylinder. In this context, the diameter of the wire is given, so the radius must be calculated by dividing the diameter by two. This concept is essential for determining the volume of the lithium wire needed to calculate its density.

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another, which is often necessary in scientific calculations. In this problem, the diameter of the wire is given in millimeters, which must be converted to centimeters to match the volume's units. Mastery of unit conversion ensures accurate calculations and consistency in measurements.