Question

An electron in n-region enters p-region with speeds $5\times10^5$ m/s and $3\times10^5$ m/s before and after barrier. Find barrier potential.

• A. 0.5 V
• B. 0.45 V
• C. 0.7 V
• D. 0.65 V

Hint:

Barrier potential equals kinetic energy loss per unit charge.

Answer 1

The Correct Option is C

Step 1: Loss in kinetic energy equals electric potential barrier energy: \[ qV = \frac{1}{2}m(v_1^2 - v_2^2) \]
Step 2: Substitute values: \[ V = \frac{1}{2} \cdot \frac{m}{e} (v_1^2 - v_2^2) \]
Step 3: \[ v_1^2 = 25\times10^{10},\quad v_2^2 = 9\times10^{10} \]
Step 4: \[ v_1^2 - v_2^2 = 16\times10^{10} \]
Step 5: \[ V = \frac{1}{2} \cdot \frac{9\times10^{-31}}{1.6\times10^{-19}} \cdot 16\times10^{10} \]
Step 6: \[ V = \frac{1}{2} \cdot 5.625\times10^{-12} \cdot 16\times10^{10} \]
Step 7: \[ V \approx 0.7\ \text{V} \]