Answer:
25.41 g/mol is molar mass of metal.
Explanation:
Number of atom in BCC unit cell = Z = 2
Density of metal = [tex]0.867 g/cm^3[/tex]
Edge length of cubic unit cell= a
= ?
Radius of the atom of metal = r = [tex]2.30\times 10^{-8} cm[/tex]
[tex]a=2\times r=2\times 2.30\times 10^{-8} cm=4.60\times 10^{-8} cm[/tex]
Atomic mass of metal =M
Formula used :
[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]
where,
[tex]\rho[/tex] = density
Z = number of atom in unit cell
M = atomic mass
[tex](N_{A})[/tex] = Avogadro's number
a = edge length of unit cell
On substituting all the given values , we will get the value of 'a'.
[tex]0.867 g/cm^3=\frac{2\times M}{6.022\times 10^{23} mol^{-1}\times (4.60\times 10^{-8} cm)^{3}}[/tex]
[tex]M = 25.41 g/mol[/tex]
25.41 g/mol is molar mass of metal.
