When a p-type semiconductor is brought into a close contact with n-type semiconductor, we get a p-n junction with a barrier potential `0.4V` and the width of depletion region is `4.0 xx 10^(-7)m`. this p-n junction is forwaed biased with a battery of voltage `3V` adn negligible internal resistance, in series with a resistance of resistance R, ideal milliammeter with reading 20 mA and key K as shown in Fig.

The resistance of resistor R is

Options

A. `1.39xx10^(5) ms^(-1)`
B. `2.78xx10^(5) ms^(-1)`
C. `1.39xx10^(6) ms^(-1)`
D. `2.78xx10^(6) ms^(-1)`

Answer

A

Explanation

Let `v_(1)` be the speed of electron when enters the depletion region and `v_(2)` is the speed when it comes out of depletion layer. According to principle of conservation of total energy,
K.E. of the incident electron =workdone against potential barrier +K.E. of the emerging electron.
i.e. `1/2mv_(1)^(2)=eV_+1/2mv_(2)^(2)`
or `1/2xx(9.1xx10^(-31))xx(4xx10^(5))^(2)`
`=(1.6xx10^(-19)xx(0.4)+1/2xx9.1xx10^(-31)xxv_(2)^(2)`
on solving, we get, `v_(2)=1.39xx10^(5) ms^(-1)`