An n-type semiconductor specimen has a Hall coefficient of 300cm3/C and its resistivity is 0.1 Ω-cm. Its electron mobility is

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UPSC IES Electrical 2022 Prelims Official Paper
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  1. 300 cm2/V-sec
  2. 30 cm2​/V-sec
  3. 3000 cm2​/V-sec
  4. 3 cm2​/V-sec

Answer (Detailed Solution Below)

Option 3 : 3000 cm2​/V-sec
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Hall effect:

The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current.

The Hall effect is used to determine carrier type, concentration, and mobility as a function of temperature.

Hall coefficient:

The Hall coefficient (RH) is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field.  

\({R_H} = \frac{\sigma }{{pe}}\) , where σ = conductivity

pe =concentration of charges.

Mobility of charges is given by \({\mu _p} = \frac{{{\sigma _p}}}{{P.e}} = {\sigma _p}.{R_H} = \frac{{{R_H}}}{\rho }\;\) 

Calculation:

The hall coefficient R= 300 cm3/C

Resistivity (ρ) = 0.1 Ω -cm

Mobility\( = {\mu _e} = \frac{{300}}{{0.1}} = 3000\) cm2/(V-sec)
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