Question

How does the relaxation time of electron in the conductor change when temperature of the counductor deacreses ?

Answer 1

When the temperature of a good conductor decreases, the number of collisions of electrons also decreases. Hence, the time of free travel increases or relaxation time increases.
                             OR
If the temperature of a good conductor decreases, its resistance decreases. Since, 

R=ρ

lA

R=ρlA

 
 

R = m

ne2

τ

lA≤0, 

 R∝ 1/τ 

 ⇒τ∝ 1/R;

R = mne2τlA≤0,  R∝ 1/τ  ⇒τ∝ 1/R;

 

so time of relaxation increases.