Tungsten has a BCC lattice and each lattice point is occupied by one atom. Calculate the metallic radius of the tungsten atom if density of tungsten is 19.30 g/cm3 and it's atomic mass is 183.9?

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Understanding Tungsten's BCC Structure
Tungsten (W) crystallizes in a Body-Centered Cubic (BCC) lattice, where each unit cell contains two atoms. To calculate the metallic radius, we will use the density and atomic mass of tungsten.
Given Data:
- Density of tungsten = 19.30 g/cm³
- Atomic mass of tungsten = 183.9 g/mol
Step 1: Calculate the Volume of the Unit Cell
Using the formula for density (D):
- D = mass/volume
The mass of one mole of tungsten is 183.9 g. Since there are 2 atoms in a BCC unit cell, the mass of the unit cell is:
- Mass of unit cell = 183.9 g/mol / Avogadro's number
Calculate the volume of the unit cell:
- Volume = Mass / Density = (183.9 g/mol / 6.022 x 10²³) / 19.30 g/cm³
Step 2: Calculate the Edge Length of the Unit Cell
The volume of the cubic cell (V) is given by:
- V = a³, where ‘a’ is the edge length.
From this, we can find the edge length:
- a = (Volume)^(1/3)
Step 3: Calculate the Atomic Radius
In a BCC structure, the relationship between the atomic radius (r) and the edge length (a) is given by:
- a = 4r / √3
Rearranging gives:
- r = (a * √3) / 4
Step 4: Conclusion
After calculating the edge length from the volume, you can substitute it back to find the metallic radius of tungsten. This radius represents the effective size of a tungsten atom in its metallic state.

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