Question

--Given Values--
Atomic Radius (nm) = 0.116
FCC Metal = Gold
BCC Metal: = Sodium
Temperature ( C ) = 1017
Metal A = Tin
Equilibrium Number of Vacancies (m^-3) = 6.02E+23
Temperature for Metal A = 369
Metal B = Gallium

1) If the atomic radius of a metal is the value shown above and it has the face-centered cubic crystal structure, calculate the volume of its unit cell in nm³? Write your answers in Engineering Notation.  
        Your Answer =
2) What is the atomic packing factor for the BCC crystal structure?  
        Your Answer =
3) Find the theoretical density for the FCC Element shown above in g/cm³. Write your answer to the ten thousandths place (0.0000):  
        Your Answer =
4) Calculate the atomic radius, in nm, of the BCC Metal above utilizing the density and the atomic weight provided by examination booklet - Write your answer with 4 significant figures:  
        Your Answer =
5) Calculate the fraction of atom sites that are vacant for copper (Cu) at the temperature provided above. Assume an energy for vacancy formation of 0.90 eV/atom:  
        Your Answer =
6) Repeat the calculation in question 5 at room temperature (25 C):  
        Your Answer =
7) Calculate the energy (in eV/atom) for vacancy formation for the Metal A and the equilibrium number of vacancies at the temperature provided above - Write your answer with 4 significant figures:  
        Your Answer =
8)Calculate the number of atoms per cubic meter in Metal B (units atoms/m³). Write your answer with 4 significant figures :
        Your Answer =
9) What is the composition, in atom percent, of an alloy that contains a) 36 g Metal A and b) 47 g Metal B? Composition for Metal A (%):
        Your Answer =
10) What is the composition, in atom percent, of an alloy that contains a) 36 g Metal A and b) 47 g Metal B? Composition for Metal B (%):  
        Your Answer =
11) What is the composition of Metal A in atom percent, if the alloy consists of 4.5 wt% Metal A and 95.5 wt% of Metal B?  
        Your Answer =
12) What is the composition of Metal B in atom percent, if the alloy consists of 4.5 wt% Metal A and 95.5 wt% of Metal B?  
        Your Answer =

Answer 1

Releation between edge length and radius of atom for FCC = a = r√8

a = edge length

r = radius of atom

a = 0.116 nm x √8

volume = a³ = (0.116 nm x √8 )³ = 0.03532 nm³ = 3.53 x 10^-2 nm³

2.

atomic packing factor = volume of atoms in unit cell / total voulme of unit cell

relation between edge length and radius for BCC = a = 4r/√3

volume of unit cell = (4r/√3)³

total no. of atoms in BCC inside unit cell = 2

volume of atoms inside unit cell = 2 x 4/3 x pi x r³

atomic packing factor = 2 x 4/3 x pi x r³ / (4r/√3)³ = 0.6798 ~ = 0.68

3.

theoretical density = mass of atoms inside cell / volume of unit cell

in FCC there are 4 atoms inside unit cell = 4 x 197g / 6.022 x 10²³ = 130.85 x 10^-23 g

volume calculated in part 1 = 3.53 x 10^-2 nm³ = 3.53 x 10^-2 x 10^-21 cm³

density = mass / volume = 130.85 x 10^-23 g / 3.53 x 10^-2 x 10^-21 cm³ = 37.06899 g/cm³

please ask rest of them seperately thanks!