Polonium with an Atomic Radius of 0.168 nm Crystallizes in a Simple Cubic Structure: What is its Density (g/cm³)?
Polonium, an element with atomic number 84 and the symbol Po, exhibits unique properties when it crystallizes in a simple cubic structure, characterized by its atomic radius of 0.168 nm. To determine its density, we must consider the relationship between atomic radius, crystal structure, and atomic mass.
For a simple cubic structure, the edge length (a) of the unit cell is directly related to the atomic radius (r) by the equation: a = 2 * r
Given the atomic radius of 0.168 nm, we can calculate the edge length:
a = 2 * 0.168 nm = 0.336 nm
The density (ρ) of a crystal can be determined using the following formula:
ρ = (M * N_A) / (V * N)
where:
- M is the atomic mass of polonium (209 g/mol)
- N_A is Avogadro's number (6.022 × 10²³ mol⁻¹)
- V is the volume of the unit cell
- N is the number of atoms in the unit cell
For a simple cubic structure, the volume of the unit cell is calculated as:
V = a³ = (0.336 nm)³ = 0.037 nm³
Since there is one atom per unit cell in a simple cubic structure, N = 1. Plugging these values into the density formula:
ρ = (209 g/mol * 6.022 × 10²³ mol⁻¹) / (0.037 nm³ * 1)
Converting nanometers to centimeters:
1 nm = 10⁻⁹ cm
We get:
ρ = (209 g/mol * 6.022 × 10²³ mol⁻¹) / (3.7 × 10⁻²⁴ cm³)
ρ ≈ 9.22 g/cm³
Therefore, the density of polonium in a simple cubic structure with an atomic radius of 0.168 nm is approximately 9.22 g/cm³.
Related Questions
- What type of crystal structure does polonium form with an atomic radius of 0.168 nm?
- How is the density of a crystal related to its atomic mass, atomic radius, and crystal structure?
- What is the volume of the unit cell for a simple cubic structure with an edge length (a) of 0.336 nm?
- How many atoms are present in a simple cubic unit cell?
- What is the density of polonium in a hexagonal close-packed structure, given its atomic radius of 0.168 nm?
Related Hot Sale Products
- Head Hexa Youth Badminton Racquet
- Yonex Astrox 88S Pro Badminton Racket
- VICTOR Thruster F Enhanced Badminton Racket
- Li-Ning Aeronaut 9000C Badminton Racket
- Carlton Airblade Elite Badminton Racquet
Pre：How does Socrates defend himself in the apology
Next：How do you spell apologize in Australia