Calculating the Weight of a Quarter-Sized Piece of Plutonium

When discussing the weight of a quarter-sized piece of plutonium, it is crucial to first determine its volume and then use the density of plutonium to calculate its weight. This article delves into the formulae involved and provides a detailed calculation.

Determining the Volume of a Quarter

The U.S. quarter has a diameter of 0.955 inches (24.26 mm) and a thickness of 0.069 inches (1.75 mm). By approximating the quarter as a cylinder, we can calculate its volume using the formula:

V πr2h

Where:

r is the radius, which is approximately 0.4775 inches (1.21 cm) h is the height or thickness, which is 0.069 inches (0.175 cm)

Converting the dimensions to centimeters:

r ≈ 1.21 cm h ≈ 0.175 cm

Substituting these values into the volume formula:

V ≈ π × (1.212) × 0.175 ≈ 0.247 cm3

Understanding the Density of Plutonium

The density of plutonium plays a critical role in determining its weight. The density of plutonium is approximately 19.86 g/cm3. It is worth noting that plutonium's density can vary depending on its allotrope and the phase it is in. For instance, plutonium used in U.S. atomic bombs is stabilized in the low-density delta phase, which has a slightly lower density of about 17 g/cm3

Weight Calculation

Using the formula for weight, we can calculate the mass of a quarter-sized piece of plutonium:

W Density × Volume

Substituting the values:

W ≈ 19.86 g/cm3 × 0.247 cm3 ≈ 4.91 grams

Therefore, a quarter-sized piece of plutonium would weigh approximately 4.91 grams. It is important to note that the actual weight can vary due to the different phases of plutonium, but this calculation provides a good approximation.

Comparison to a Regular Quarter

A regular U.S. quarter dollar piece is made of nickel-plated copper with a density of 8.9 g/ml and a mass of 5.9 g. The volume of a quarter is approximately 0.6629 cm3. This means a quarter-sized piece of plutonium, based on the aforementioned density, would weigh about twice as much as a normal quarter, approximately 11.3 grams.

The exact weight can vary by up to 25% depending on the specific phase of plutonium. For a more precise calculation, one would need to know the exact phase of the plutonium.

Understanding the weight of plutonium and its density is crucial in various fields, including nuclear science and engineering. This information can be vital for those working with plutonium or those interested in the properties and applications of this unique material.