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Chapter 19: Problem 2620

The ratio of concentration of electrons and holes in a semi-conductor is $(7 / 5)\( and the ratio of currents is \)(7 / 4)$, then what is the ratio of their drift velocities? (A) \((4 / 5)\) (B) \((5 / 6)\) (C) \((4 / 5)\) (D) \((5 / 4)\)

Short Answer

Expert verified
The correct answer is (D) \(\frac{5}{4}\).

Step by step solution

01

Identify the relationship between current, concentration, and drift velocity

The current (I) in a semiconductor is related to the concentration (n) and drift velocity (v_d) of charge carriers through the formula: \(I = qnAv_d\) where: - q is the charge of an electron, - n is the concentration of carriers, - A is the cross-sectional area of the semiconductor, - v_d is the drift velocity of carriers.
02

Rewrite the relationship using the given ratios

We will use the formula for current in terms of concentration and drift velocity to express the given ratios: \(I_e / I_h = \frac{q n_e A v_{d_e}}{q n_h A v_{d_h}}\) where _e and _h subscripts refer to electrons and holes respectively. Given the ratio of concentrations: \(n_e/n_h = 7/5\) Given the ratio of currents: \(I_e/I_h = 7/4\) Plug these ratios into the formula for current ratio: \(\frac{7}{4} = \frac{(7/5) v_{d_e}}{v_{d_h}}\)
03

Solve for the ratio of drift velocities

Now, our goal is to find the ratio \(v_{d_e} / v_{d_h}\). So we rearrange the equation to isolate this ratio and simplify: \(\frac{v_{d_e}}{v_{d_h}} = \frac{7/4}{7/5}\) \(\frac{v_{d_e}}{v_{d_h}} = \frac{5}{4}\)
04

Compare the answer with the given options

Now that we have calculated the ratio of drift velocities, we have: \(\frac{v_{d_e}}{v_{d_h}} = \frac{5}{4}\) Comparing with the given options, we observe that this ratio matches with option (D). So, the correct answer is (D) \((5/4)\).

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