Question

A potential barrier of $0.5\text{V}$ exists across a $p-n$ junction. An electron with speed $5.0\times {10}^5{\text{ms}}^{-1}$ approaches the $p-n$ junction from $n-$side with what speed will it enter the $p-$side?
$(\text{Mass of the electron,}m=9.1\times {10}^{-31}\text{kg})$

• A. $4\times {10}^5{\text{ms}}^{-1}$
• B. $2.7\times {10}^5{\text{ms}}^{-1}$
• C. $1.8\times {10}^5{\text{ms}}^{-1}$
• D. $2.7\times {10}^4{\text{ms}}^{-1}$

Answer 1

The correct option is B $2.7\times {10}^5{\text{ms}}^{-1}$

Suppose the electron has a speed $v_1$ when it enters the depletion layer and $v_2$ when it comes out of it.

As the electron moves against the electric field in the depletion region, the electrostatic potential energy of the electron increases by,

$\Delta U=e\times 5\text{V}=5\text{eV}$.

From the principle of conservation of energy,

$\frac{1}{2}m{v}_1^2=0.5\text{eV}+\frac{1}{2}m{v}_2^2$

Substituting the values,

$\Rightarrow \frac{1}{2}\times (9.1\times {10}^{-31}\text{kg})\times (5\times {10}^5{\text{ms}}^{-1}{)}^2=0.5\times 1.6\times {10}^{-19}\text{J}+\frac{1}{2}(9.1\times {10}^{-31}\text{kg})v_2^2$
$\Rightarrow 1.13\times {10}^{-19}\text{J}=0.8\times {10}^{-19}\text{J}+(4.55\times {10}^{-31})v_2^2$

$\Rightarrow v_2=2.7\times {10}^5{\text{ms}}^{-1}$

Hence, $\left(B\right)$ is the correct answer.

Why this question? Tip: When the force is conservative in nature, the principle of conservation of energy can be used.

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