JEE Main · 2006 · 30 Apr 2006 · Offline · Semiconductors

If the ratio of the concentration of electrons that of holes in a semiconductor is

\frac{7}{5}

and the ratio of currents is

\frac{7}{4}

, then what is the ratio of their drift velocities?

(A) $\frac{4}{7}$
(B) $\frac{5}{8}$
(C) $\frac{4}{5}$
(D) $\frac{5}{4}$ ✓ Correct

Answer: (D)

Solution

The total current is carried by both electrons and holes, each contribution being (number density) times (charge) times (drift speed). Taking the ratio for the two carriers,

\frac{I _{e}}{I _{h}} = \frac{n _{e} v _{e}}{n _{h} v _{h}}

, so

\frac{v _{e}}{v _{h}} = \frac{I _{e} / I _{h}}{n _{e} / n _{h}} = \frac{7/4}{7/5} = \frac{5}{4}

. The electrons drift

\frac{5}{4}

times as fast as the holes.

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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