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Chapter 27: Q. 17 (page 762)

17. What is the mean time between collisions for electrons in (a) an aluminum wire and (b) an iron wire?

Short Answer

Expert verified

(a) The mean time between collisions for electrons in an aluminum wire is $1.46 \times 10^{- 14} s$ .

(b) The mean time between collisions for electrons in an iron wire is $4.18 \times 10^{- 14} s$ .

Step by step solution

01

Given information Part (a)

The mean time between collisions for electrons in an aluminum wire.

02

Explanation Part (a)

The conductivity is given as $σ = \frac{n_{e} e^{2} τ}{m}$
The mean time between collisions parametric as $τ = \frac{m σ}{n_{e} e^{2}}$
In the case of aluminum, calculate to be,
$τ = \frac{9.1 \times 10^{- 31} \times 3.5 \times 10^{7}}{6.0 \times 10^{28} \times {(1.6 \times 10^{- 19})}^{2}}$

$= 1.46 \times 10^{- 14} s .$

03

Final answer Part (a)

The mean time between collisions for electrons in an aluminum wire is $1.46 \times 10^{- 14} s$ .

04

Given information Part (b)

The mean time between collisions for electrons in an iron wire.

05

Explanation Part (b)

The mean time of iron,
$τ = \frac{9.1 \times 10^{- 31} \times 1 \times 10^{7}}{8.5 \times 10^{28} \times {(1.6 \times 10^{- 19})}^{2}}$

$= 4.18 \times 10^{- 14} s$

06

Final Answer Part(b)

The mean time between collisions for electrons in an iron wire is $4.18 \times 10^{- 14} s$ .

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Most popular questions from this chapter

a. How many conduction electrons are there in a $1.0 mm$ diameter gold wire that is $10 cm$ long?

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