Potential difference of 100 V is applied to the ends of a copper wire one metre long. Calculate the average drift velocity of the electrons ? Compare it with thermal velocity at `27^@C`. Consider there is one conduction electron per atom. The density of copper is `9.0xx10^(3)kg//m^(3)`, Atomic mass of copper is 63.5 g. Avogadro's number `= 6.0 xx 10^(23)` per gram-mole. Conductivity of copper is `5.81 xx 10^(7)Omega^(-1)m^(-1)`. Boltzmann constant `= 1.38 xx10^(23)JK^(-1)`.

Explanation

Since `DeltaV=100V, l=1m`,
`therefore` electric field = `(DeltaV)/(l)=(100)/(1)=100Vm^(-1)`
Also, conductivity `sigma=5.81xx10^(7)Omega^(-1)m^(-1)`
`n=8.45xx10^(28)m^(-3)`
`v_(d)=(sigma)/(en)E=(5.81xx10^(7)xx100)/(1.6xx10^(-19)xx8.45xx10^(28))=0.43ms^(-1)`
Thermal velocity can be calculated considering electrons as ideal gas particles.
`v_(rms)=sqrt((3k_(B)T)/(m))=sqrt((3xx(1.38xx10^(-23))300)/(9.1xx10^(-31)))`
(where `k_(B)` is the Boltzmann constant)
`v_(rms)=1.17xx10^(5)ms^(-1)`