In a semiconductor, the number density of intrinsic charge carries at 27$$^\circ$$C is 1.5 $$\times$$ 10¹⁶/m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5 $$\times$$ 10²²/m³. The electron density in the doped semiconductor is ___________ $$\times$$ 10⁹/m³.

In a given circuit diagram, a 5 V zener diode along with a series resistance is connected across a 50 V power supply. The minimum value of the resistance required, if the maximum zener current is 90 mA will be __________ $$\Omega$$.

A zener diode having zener voltage 8 V and power dissipation rating of 0.5 W is connected across a potential divider arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance R_p is .................... $$\Omega$$.

For the forward biased diode characteristics shown in the figure, the dynamic resistance at I_D = 3 mA will be __________ $$\Omega$$.