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Sagot :
The unit cell volume of the crystal is [tex]V_c = 9.9084*10^-^2^3 cm^3 / unit cell[/tex] and the density of titanium is calculated as 4.71g/cm^3 while the literature value is 4.5 g/cm^3
Data;
- radius = 0.1445 nm
- c/a = 1.58
- A = 46.88 g/mol
Unit Cell Volume
The unit cell volume can be calculated as
[tex]V_c = 6R^2c\sqrt{3}\\[/tex]
let's substitute the values into the formula
[tex]V_c = 6 * (1.445*10^-^8)^2 * 1.58 8 * a * \sqrt{3} \\a = 2R\\V_c = 6 * (1.445*10^-^8)^2 * 1.58* 2 * 1.445*10^-^8 * \sqrt{3}\\ V_c = 9.984*10^-^2^3 cm^3 / unit cell[/tex]
The unit cell volume of the crystal is [tex]V_c = 9.9084*10^-^2^3 cm^3 / unit cell[/tex]
Density of Ti
The density of titanium can be calculated as
[tex]\rho = \frac{nA}{V_c N_a}[/tex]
- n = 6 for hcp
- A = 46.88 g/mol
- Na = Avogadro's number
let's substitute the values into the formula
[tex]\rho = \frac{nA}{V_c Na}\\ \rho = \frac{6*46.88}{9.9084*10^-^2^3* 6.023*10^2^3} \\\rho = 4.71 g/cm^3[/tex]
The density of titanium is calculated as 4.71g/cm^3 while the literature value is 4.5 g/cm^3
Learn more on crystal lattice here;
https://brainly.com/question/6610542
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