Question

If an electron approaches the $p-n$ junction from the $n$-side with a speed of $5 \times 10^5\, m \,s^{-1}$, with what speed will it enter the $p$-side?

• A. $5\times 10^5 \,m/s$
• B. $2.5\times 10^6 \,m/s$
• C. $2.7\times 10^5 \,m/s$
• D. $1\times 10^5 \,m/s$

Answer 1

Answer: (C)

Suppose an electron enters the depletion layer with speed $v_1$ and $p$-region with speed $v_2$, as shown in figure.

potential energy increased by $eV$ joule.
By energy conservation;
$\frac{1}{2}mv_{2}^{2} + eV = \frac{1}{2}mv_{1}^{2}$ or
$ \frac{1}{2}mv_{2}^{2} = \frac{1}{2} mv_{1}^{2} - eV $
$= \frac{1}{2}\times 9.1 \times 10^{-31} \left(5.0 \times10^{5}\right)^{2} - 1.6 \times10^{-19} \times 0.50 $
$ = \left(1.13 - 0.8\right)\times 10^{-19} $
$ = 0.33\times 10^{-19} J $
$ = V_{2}^{2} = \frac{2\times 0.33\times 10^{-19}}{m}$
$ = \frac{0.66\times 10^{-19}}{9.1\times 10^{-31}} $
$ = 7.25\times 10^{10} $
or $v_{2} = 2.7\times 10^{5} ms^{-1}$