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An $N -$ type silicon sample of length $6 \times 10^{- 2} m$ has width $4 \times 10^{- 3} m$ and thickness $25 \times 10^{- 5} m .$ When a voltage is applied across the length of the sample, the current in sample is 4.8 mA. If the free electron density in sample is $10^{22} m^{- 3},$ then the time taken for the electrons to travel the full length of the sample in seconds is t. Find 400 t.

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answer is 8.

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Detailed Solution

$J = \frac{I}{A} = \frac{4.8 \times 10^{- 3}}{(4 \times 10^{- 3}) (25 \times 10^{- 5})} = 4800 A / m^{2}$

Drift velocity, $υ_{d} = \frac{J}{n e} = \frac{4800}{10^{22} \times (1.6 \times 10^{- 19})} = 3.0 m s^{- 1}$

Time taken $t = \frac{l}{υ_{d}} = \frac{6 \times 10^{- 2}}{3.0} = 0.02 s ∴ 400 t = 8$

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