# Electrons in Silver

The resistivity of a $Ag$ conductor at room temperature is $\rho =1.54*10^{-8} \Omega*m$ and the electron concentration is $n =5.8*10^{28} m^{-3}$. Find the following:

a) the average time $\tau$ between two collisions of the electrons with the lattice.

b) the mobility $\mu$ of the conduction electrons

c) the electrons drift (transport) speed

(The mass $m_0$ and the charge $e$ of electrons are given).

a) The average time between two consecutive collisions can be found from the expression of electric conductivity:

$\sigma = (1/\rho) = (n e^2\tau)/m_0$

$\tau = m_0/(n e^2\rho) =3.98*10^{14} s$

b) The mobility of the electrons is given by the relation

$\nu =(e\tau)/m_0 =1/(en\rho) =7*10^{-3} m^2/(V*s)$

c) The drift velocity of electrons under electric field $E$ is

$v_d =\mu*E = 7*10^{-4} m/s$