The atoms of two elements have the same atomic radius and they are packed together the same way. What information would you need to determine which one is more dense?
The correct answer and explanation is:
Answer:
To determine which element is more dense, you would need to know the atomic mass (or atomic weight) of each element.
Explanation (300 words):
Density is defined as mass per unit volume. When comparing two elements that have the same atomic radius and are packed in the same way (i.e., the same crystal structure and packing arrangement), their volume per atom is effectively the same. This is because atomic radius influences the size of each atom, and packing arrangement determines how atoms occupy space in the solid.
Since the volume per atom is the same for both elements, the difference in density will come down to the mass of each atom. The heavier atom (with the greater atomic mass) will make the element denser because each atom contributes more mass within the same volume.
In summary, the key factors are:
- Atomic Radius: Same for both elements, so atoms have similar size.
- Packing Arrangement: Same for both elements, so atoms are arranged to occupy space similarly.
- Atomic Mass: Different, and this determines the mass per atom.
To calculate density, you would use the formula: Density=Mass per atom×Number of atoms per unit volumeVolume\text{Density} = \frac{\text{Mass per atom} \times \text{Number of atoms per unit volume}}{\text{Volume}}
Given the same atomic radius and packing, the number of atoms per unit volume and volume are constant. So the mass per atom (atomic mass) becomes the decisive factor.
For example, if element A has an atomic mass of 50 u and element B has an atomic mass of 100 u, element B will be twice as dense as element A under the given conditions.
In short: To determine which element is denser when atomic radius and packing are the same, you only need to know their atomic masses. The element with the higher atomic mass will be more dense.