If an electron approaches the $p-n$ junction with potential barrier 0.50 V , from the $n$-side with

Question

If an electron approaches the $p-n$ junction with potential barrier 0.50 V , from the $n$-side with a speed of $5 	imes 10^5 \mathrm{~m} \mathrm{~s}^1$, with what speed will it enter the $p$-side?

Professor PC Thomas Classes · Answer

(c) : Suppose an electron enters the depletion layer with speed $v_1$ and $p$-region with speed $v_2$, as shown in figure. Its potential energy increased by eV joule. By energy conservation  \ $\frac{1}{2} m v_2^2+e V=\frac{1}{2} m v_1^2$ or $\frac{1}{2} m v_2^2=\frac{1}{2} m v_1^2-e V$\ $=\frac{1}{2} 	imes\left(9.1 	imes 10^{-31}ight)\left(5.0 	imes 10^5ight)^2-1.6 	imes 10^{-19} 	imes 0.50$\ $=(1.13-0.8) 	imes 10^{-19}=0.33 	imes 10^{-19} \mathrm{~J}$\ $	herefore \quad v_2^2=\frac{2 	imes 0.33 	imes 10^{-19}}{m}=\frac{0.66 	imes 10^{-19}}{9.1 	imes 10^{-31}}=7.25 	imes 10^{10}$\ or $\quad v_2=2.7 	imes 10^5 \mathrm{~m} \mathrm{~s}^{-1}$.