Respuesta :
Answer:
For a: The mass of one unit cell of copper is [tex]1.0553\times 10^{-22}g[/tex]
For b: The volume of copper unit cell is [tex]4.726\times 10^{-23}cm^3[/tex]
For c: The edge length of the unit cell is [tex]3.615\times 10^{-8}cm[/tex]
For d: The radius of a copper atom 127.82 pm.
Explanation:
- For a:
We know that:
Mass of copper atom = 63.55 g/mol
According to mole concept:
1 mole of an atom contains [tex]6.022\times 10^{23}[/tex] number of atoms.
If, [tex]6.022\times 10^{23}[/tex] number of atoms occupies 63.55 grams.
So, 1 atom will occupy = [tex]\frac{63.55g}{6.022\times 10^{23}atom}\times 1 atom=1.0553\times 10^{-22}g[/tex]
Hence, the mass of one unit cell of copper is [tex]1.0553\times 10^{-22}g[/tex]
- For b:
Copper crystallizes with a face-centered cubic lattice. This means that 4 number of copper atoms are present in 1 units cell.
Mass of 4 atoms of copper atom = [tex]1.0553\times 10^{-22}g/atom \times 4atoms=4.2212\times 10^{-22}g[/tex]
We are given:
Density of copper = [tex]8.93g/cm^3[/tex]
To find the volume of copper, we use the equation:
[tex]\text{Density of copper}=\frac{\text{Mass of copper}}{\text{Volume of copper}}[/tex]
Putting values in above equation, we get:
[tex]8.93g/cm^3=\frac{4.2212\times 10^{-22}}{\text{Volume of copper}}\\\\\text{Volume of copper}=4.726\times 10^{-23}cm^3[/tex]
Hence, the volume of copper unit cell is [tex]4.726\times 10^{-23}cm^3[/tex]
- For c:
Edge length of the unit cell is taken as 'a'
Volume of cube = [tex]a^3[/tex]
Putting the value of volume of unit in above equation, we get:
[tex]\sqrt[3]{4.726\times 10^{-23}}cm^3=3.615\times 10^{-8}cm[/tex]
Hence, the edge length of the unit cell is [tex]3.615\times 10^{-8}cm[/tex]
- For d:
The relation of radius and edge length for a face-centered lattice follows:
[tex]a=r\sqrt{8}[/tex]
Putting values in above equation, we get:
[tex]3.615\times 10^{-8}=r\sqrt{8}\\\\r=1.2782\times 10^{-8}cm[/tex]
Converting cm to pm, we get:
[tex]1cm=10^{10}pm[/tex]
So, [tex]1.2782\times 10^{-8}cm=127.82pm[/tex]
Hence, the radius of a copper atom 127.82 pm.
