Question

Analyzing Data Osmium is the element with the greatest density, 22.58 \(\mathrm{g} / \mathrm{cm}^{3}\) . How does the density of osmium compare to the density of a typical nucleus of \(2 \times 10^{8}\) metric tons/cm \(^{3} ?(1 \text { metric ton }=1000 \mathrm{kg})\)

Short answer

The density of a typical nucleus is approximately \(8.86 \times 10^{12}\) times greater than the density of osmium.

Step-by-step solution

- Convert Metric Tons to Grams

First, convert the density of the typical nucleus to grams per cubic centimeter. Since 1 metric ton is equal to 1000 kg, and 1 kg is equal to 1000 grams, 1 metric ton is equal to 1,000,000 grams. Thus, the density of the typical nucleus is \(2 \times 10^8 \text{ metric tons/cm}^{3} \times 1,000,000 \text{ grams/metric ton} = 2 \times 10^{14} \text{ grams/cm}^{3}\).

- Compare Densities

Now, compare the density of osmium to the density of the typical nucleus. The density of osmium is 22.58 \(\text{grams/cm}^{3}\). The density of the typical nucleus is \(2 \times 10^{14} \text{ grams/cm}^{3}\).

- Calculate Density Ratio

Calculate the ratio of the density of the typical nucleus to the density of osmium: \(\frac{2 \times 10^{14}}{22.58} \approx 8.86 \times 10^{12} \). This means that the density of a typical nucleus is approximately \(8.86 \times 10^{12}\) times greater than the density of osmium.

Key concepts

density conversion

Density conversion helps us understand and compare different materials. It can be tricky without the right steps. For instance, in our example, to compare the density of osmium and a nuclear density, we change units.
This exercise takes the density of a nucleus given in metric tons per cubic centimeter, a large unit. We need to convert this to grams per cubic centimeter.
Here are the key steps for such conversions:

• Identify the units given and the units for conversion.
• Use known relationships: For example, 1 metric ton = 1000 kg and 1 kg = 1000 grams.
• Calculate step-by-step: In our case, 1 metric ton = 1,000,000 grams.

Following these steps, the nuclear density becomes 2 x 10^8 metric tons/cm³ x 1,000,000 g/metric ton = 2 x 10^14 g/cm³.
With these conversions, we can now compare densities accurately.

nuclear physics

Nuclear physics explores the building blocks of the universe, focusing on protons and neutrons in the nucleus of atoms.
One key concept in nuclear physics is that nuclei are extremely dense. This is mostly due to the fact that nuclei are packed tight with particles.
In our example, the nucleus's density is 2 x 10^14 grams per cubic centimeter compared to osmium at roughly 22.58 grams per cubic centimeter. Notice how drastic the difference is.
Understanding this greatly helps in fields such as nuclear energy and medical imaging. For such comparisons in nuclear physics:

• Always use precise measurements.
• Convert units where necessary for easier comparisons.
• Acknowledge the incredibly high densities involved.

High nuclear density is crucial for phenomena like nuclear fission where a significant amount of energy is released from tiny amounts of mass.

metric system

The metric system is a universal method of measurement used worldwide. It includes units like meters, kilograms, and liters.
In science, this system is essential for consistent and accurate communication. Units in the metric system are based on powers of ten, making conversion straightforward.
Let's convert metric tons to grams: 1 metric ton = 1000 kg. To get to grams, remember 1 kg = 1000 grams. Therefore, 1 metric ton equals 1,000,000 grams.
For the given problem:

• Start with the original density: 2 x 10^8 metric tons/cm³.
• Convert to grams: Multiply by 1,000,000 grams/metric ton.
• Result is 2 x 10^14 grams/cm³.

Using the metric system simplifies measurements and conversions, especially when dealing with large or small magnitudes in scientific contexts. It helps ensure clarity and precision.