Answer:
Step-by-step explanation:
Given:
Area, A = 5 × 10^-6 m^2
Current, I = 30 A
U = (m × σ × V)/ρ × e × f × l)
= I/(n × A × Q)
Where,
u is again the drift velocity of the electrons, in m⋅s−1
m is the molecular mass of the metal, in kg
σ is the electric conductivity of the medium at the temperature considered, in S/m.
ΔV is the voltage applied across the conductor, in V
ρ is the density (mass per unit volume) of the conductor, in kg⋅m−3
e is the elementary charge, in C
f is the number of free electrons per atom
ℓ is the length of the conductor, in m
A.
Molar mass of iron = 56 g/mol
Converting g to kg,
56 g/mol × 1 kg/1000 g
= 0.056 kg/mol
= approx. 0.056 kilograms in 1 mole of iron.
B.
Density, ρ = 7874 kg/m^3
Molar density = density, ρ/molar mass
= 7874/0.056
= 1.406 × 10^5 mol/m^3
C.
Avogadros constant, Na = 6.022 × 10^23 atoms/mol
Density of iron atoms = avogadros constant × molar density
= 6.022 × 10^23 × 1.406 × 10^5
= 8.478 × 10^28 atoms/m^3
D.
Fe --> Fe2+ + 2e-
density of conduction electrons = 2 conduction electrons/1 atom of iron
= 2 × 8.478 × 10^28
= 1.69 × 10^29 conduction electrons/m^3
E.
Q = 1.602 × 10^-19 C
Using the equation above,
V = 30/(1.69 × 10^29 × 1.602 × 10^-19 × 5 × 10^-6)
= 2.216 × 10^-4 m/s.