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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), Atomic mass of copper is 63.5g. Avogadro's number =6.0xx10^(23) per gram - mole. Conductivity of copper is 5.81xx10^(7)Omega^(-1). Boltzmann constant =1.38xx10^(-23)KJ^(-1). |
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Answer» SOLUTION :Since `6XX10^(23)` copper atoms have a MASS of 63.5 g, and there is one conduction electron per atom, so number of electrons per unit volume is `n=(6.0xx10^(23))/(63.5xx10^(-3))xx9.0xx10^(3)kg//m^(3)=8.5xx10^(28)m^(-3)` `"Electric field "E=(V)/(l)=(100)/(1)=100Vm^(-1)` As `J=sigma E=n ev_(d)` `therefore v_(d)=(sigmaE)/(n e)=((5.81xx10^(7))xx(100))/((8.5xx10^(28))xx1.61xx10^(-19))=0.43 ms^(-1)` `"Thermal velocity "v_("rms")=sqrt((3k_(B)T)/(m_(e)))` `=sqrt((3xx1.38xx10^(-23)xx300)/(9.1xx10^(-31))=1.17xx10^(5)m//s` `(upsilon_(d))/(upsilon_("rms"))=(0.43)/(1.17xx10^(5))=3.67xx10^(-6)` |
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