Question

The mean free path of conduction electrons in copper is about $4\times {10}^{-8}m$. For a copper block, find the electric field which can give, on an average, $1eV$ energy to a conduction electons.

• A. $2.5\times {10}^7{\text{Vm}}^{-1}$
• B. $2.5\times {10}^{-7}{\text{Vm}}^{-1}$
• C. $5\times {10}^{-7}{\text{Vm}}^{-1}$
• D. $2.5\times {10}^{-7}{\text{Vm}}^{-1}$

Answer 1

The correct option is A $2.5\times {10}^7{\text{Vm}}^{-1}$

Let the electric field Be E. The force on an electron is eE. As the electron moves through a distance d, the work done on it is eEd. This is equal to the energy transeferred to the electron. As the electron travels an average distance of $4\times {10}^{-8}m$ before a collision, the energy transfered is eE $(4\times {10}^{-8}m)$. To get $1eV$ energy from the electric field,
$eE(4\times {10}^{-8}m)=1eV$
or, $E=2.5\times {10}^7{\text{Vm}}^{-1}$
$\begin{array}{c}\text{Why this question?}\\ \text{Tip:The mean free path is the average distance travelled by an electron before collision.}\end{array}$