Question

Aluminium has three valence electrons per atom, an atomic weight of 0.02698 kg mol−1,
a density of 2700kgm-3, and a conductivity of 3.54× 107 W−1m−1. Calculate the relaxation
time in Aluminium.

Answer 1

Answer on Question #51239, Physics, Solid State Physics

Task: Aluminium has three valence electrons per atom, an atomic weight of 0.02698 kg mol $^{-1}$, a density of 2700 kgm $^{-3}$, and a conductivity of 3.54× 10 $^{7}$ Ω $^{-1}$ m $^{-1}$. Calculate the relaxation time in Aluminium

Solution:

Given, Atomic weight=0.02698 kg mol $^{-1}$; density D=2.7*10 $^3$ kgm $^{-3}$; conductivity σ=3.54× 10 $^7$ Ω $^{-1}$ m $^{-1}$; Avagadro number Na=6.022*10 $^{23}$ mol $^{-1}$

$$\sigma = \frac{n e^{2} \tau}{m}$$ $$n = (\text{number of free electrons} \cdot N_{A} \cdot D) / (\text{Atomic weight}) = \frac{3 \cdot 6.02 \cdot 10^{23} \cdot 2.7 \cdot 10^{3}}{0.02698} m^{-3} \approx 18.08 \cdot 10^{28} m^{-3}$$ $$\text{Thus, } \tau = \frac{\sigma m}{n e^{2}} = \frac{3.54 \cdot 10^{7} \cdot 4.48 \cdot 10^{-31}}{18.08 \cdot 10^{28} \cdot (1.6 \cdot 10^{-19})^{2}} = 0.34 \cdot 10^{-14} s$$

Answer: $\tau = 0.34 \cdot 10^{-14} s$

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