Question : If resitivity of copper is 1.7×10-8 Ωm, then its mobility will be approximately (take density of electrons in copper 8.5×1028 /m³ and charge on electron 1.6×10-19 C)
(i) 4.3×10-3 m²/C-Ω
(ii) 6.8×10-3 m²/C-Ω
(iii) 8.5×10-3 m²/C-Ω
(iv) 3.4×10-3 m²/C-Ω
Doubt by Ridhi
Solution :
ρ=1.7×10-8 Ωm
n=8.5×1028 /m³
ρ=1.7×10-8 Ωm
n=8.5×1028 /m³
We know
j=σE
I/A=σE [∵j=I/A]
I=σEA
neVdA=σEA [∵I=neVdA]
neVd=σE
ne[Vd/E]=σ
neµ=σ [∵Vd/E=µ]
µ=σ/ne
µ=[1/ρ]/ne [∵σ=1/ρ]
µ=1/ρne
I/A=σE [∵j=I/A]
I=σEA
neVdA=σEA [∵I=neVdA]
neVd=σE
ne[Vd/E]=σ
neµ=σ [∵Vd/E=µ]
µ=σ/ne
µ=[1/ρ]/ne [∵σ=1/ρ]
µ=1/ρne
µ=1/[(1.7×10-8)×(8.5×1028)×(1.6×10-19)]
µ=1/[1.7×8.5×1.6×10-8+28-19]
µ=1/[1.7×8.5×1.6×10]
µ=1000/(17×85×16×10]
µ=100/23120
µ=1/[1.7×8.5×1.6×10-8+28-19]
µ=1/[1.7×8.5×1.6×10]
µ=1000/(17×85×16×10]
µ=100/23120
µ=0.00432525951
µ=4.3×10-3 m²/C-Ω
µ=4.3×10-3 m²/C-Ω
Hence, (i) 4.3×10-3 m²/C-Ω, would be the correct option.
