Drift velocity formula Steps:

• Use $v_d = \frac{I}{n e A}$, where $I = 50 \times 10^{-6}$ A, $n = 2.0 \times 10^{13}$ cm⁻³ (standard for Ge), $e = 1.6 \times 10^{-19}$ C, $A = 1$ cm².
• Compute $n e A = 2.0 \times 10^{13} \times 1.6 \times 10^{-19} \times 1 = 3.2 \times 10^{-6}$ C/cm.
• Then $v_d = \frac{5.0 \times 10^{-5}}{3.2 \times 10^{-6}} = 15.6$ cm/s.
• Convert to m/s: 0.156 m/s ≈ 0.15 m/s. Why A is correct:
• Matches $v_d = \frac{I}{n e A}$ from definition of current in terms of carrier motion. Why the others are wrong:
• B is 10 times larger, from underestimating n by factor of 10.
• C is 120 times larger, from using metallic n ≈ 10^{22} cm⁻³.
• D is unrealistically large, approximating thermal speeds instead of drift.

Final answer: A