If \(\rho \)is the resistivity of pure semiconductor.
then \(\frac { 1 }{ \rho } =e(n_{ e }\mu _{ e }+n_{ h }\mu _{ h })=en_{ i }[\mu _{ e }+\mu _{ h }]\)
\(\therefore \) For pure semiconductor
,\(n_{ e }=n_{ h }={ n }_{ i }\)
\( or \ { n }_{ i }=\frac { 1 }{ e\rho (\mu _{ e }+\mu _{ h }) } \)
\(=\frac { 1 }{ (1.6\times10^{ -19 })\times0.54\times(0.24+.18)}\)
\(=2.76\times10^{ 19 }m^{ -3 }\)
When \(10^{ 20 }\)acceptor atoms are further doped in semiconductor,
then \(n_{ h }-n_{ e }={ N }_{ a }-N_{ d }={ 10 }^{ 20 }-2.76\times10^{ 19 }\)
\(=7.24\times10^{ 19 }m^{ -3 }\)
As \(n_{ h }>n_{ e }\)the material is p-type semiconductor.
Now  \(n_{ h }=7.24\times10^{ 19 }m^{ -3 }\)
Resistivity \(\rho =\frac { 1 }{ en_{ h }\mu _{ h } }\)
\( =\frac { 1 }{ (1.6 \times 10^{ -19 })\times(7.24\times10^{ 19 })\times0.18 } \)
\( =0.479\Omega m\)

196.43 V

(i) 0.1mA (ii) 6.9mA
\(\beta =\frac { I_{ c } }{ I_{ b } } \) or \(\beta =\frac { I_{ c } }{ I_{ b } } \ I_{ c }=\beta I_{ b }=69 \ I_{ b }\)
\({ I }_{ e }=I_{ b }+I_{ c }=I_{ b }+69I_{ b }=70 \ I_{ b }\)
\(\therefore \) \(7.0=70I_{ b }\) or \(I_{ b }=\frac { 7.0 }{ 70 } =0.1 \ mA\)
\(I_{ c }={ I }_{ e }-I_{ b }=7.0-0.1=6.9 \ mA\)

(i) \(52.1\Omega m\) 
(ii) \(138.9\Omega m\)

(i) \(4.63\times 10^{ 20 }\ m^{ -3 }\),
(ii) \(1.3\times 10^{ 21 }\ m^{ -3 }\)
(i) \(\frac { 1 }{ \rho } =en_{ e } \ \mu _{ e } \ or \ n_{ e }=\frac { 1 }{ \rho e\mu _{ e } } \) 
(ii) \(n_{ h }=\frac { 1 }{ \rho e\mu _{ h } } \)

(a), (b), (d)
Electrons and holes are not present in depletion layer hence recombination cannot take place.

Voltage gain of the first amplifier, V₁ = 10
Voltage gain of the second amplifier, V₂ = 20
Input signal voltage, V_i = 0.01 V
Output AC signal voltage = V_o
The total voltage gain of a two-stage cascaded amplifier is given by the product of voltage gains of both the stages, i.e.,
V = V₁ x V₂
= 10 x 20 = 200
We have the relation:
\(V=\frac{V_{0}}{V_{1}}\)
V₀ = V x V_i
= 200 x 0.01 = 2 V
Therefore, the output AC signal of the given amplifier is 2 V.

The four valence electrons of carbon are present in second orbit while that of silicon in third orbit. So, energy required to extricate an electron from silicon is much smaller than carbon. Therefore, the number of free electrons for conduction in silicon is significant on contrary to the carbon. This makes silicons is conductivity much higher than carbon. This is the main distinguishable property.

When we apply sufficient voltage to LED, electron move across the junction into p-region and get attracted to the holes there holes are sent from p region to n region (where they are minority carriers). Thus, electrons and holes recombine During each recombination, the electric potential energy is converted into the electromagnetic energy and photon of light with a characteristic frequency is emitted, this is how, LED works.

Advantages of LEDs over incandescent lamps
(i) Since, LEDs do not have a filament that can burn out, hence, they last longer.
(ii) They do not get hot during use, hence fast action no warm-up time required. Hand calculators, cash registers, digital clocks, etc. use seven-segment red or green displays. Each segment is an LED and depending on which segment is energised, the display lights up the numbers 0 to 9, as shown in figure.

As, car enters in the gate, any one or both are opened. The device is shown below:

So, OR gate gives the desired output

The logic gate P is NAND gate and Q is OR gate. The truth table is given by

When an \(npn\) transistor with common emitter mode is used as a switch, then if during working, there is no collector current, then the transistor is in cut off  state. In case of silicon-transistor, so long as input voltage \(V_{ i }<0.6V\), the transistor will be in cut off state.
If during working, there is a situation, beyond cut off state, for which \(V_{ i }<0.6V\) but less than 1.0 V the collector current increases almost linearly and the output voltage decreases linearly, till \(V_{ i }\) becomes nearly 1.0 V. The transistor in this state is called in active state. If during working, there is a situation beyond active state for which \(V_{ i }>1.0V\) , the variation of \(V_{ i }\) and \(V_{ o }\) is non-linear, because with the increase in \(V_{ i }\) , \(V_{ o }\)  is found to decrease towards zero, but never becomes zero. In this situation the collector current \(I_{ C }\) becomes maximum and the transistor is in a saturation state.
When a transistor is being used as a switch, it will not remain in active state.

\(\beta =I_{ c }/I_{ b }=10^{ -3 } \ / \ (20\times 10^{ -6 })=50 \ ;\)
Voltage gain, \(A_{ V }=\beta \frac { R_{ C } }{ R_{ i } } =50\times \frac { 4000 }{ 1000 } =200\)

Transistor is said to be in active state when its emitter-base junction is suitably forward biased and base-collector junction is suitably reverse biased.

No, because the voltmeter to be used to measure potential difference across the p-n must have a very high resistance as compared to junction resistance, which is nearly infinite, if not biased. Apart from it, there are no free charge carriers in the depletion region of p-n junction.

Hole is seat of positive charge which is produced when an electron breaks away from a covalent bond in a semiconductor.
Characteristics of a hole
1. Hole carries a unit positive charge.
2. It has the same magnitude of charge as that of electron.
3. Energy of a hole is high as compared to that of electron.
4. The mobility of hole is smaller than that of electron.
5. In external electric field holes move in a direction opposite to that of electron.

(i) SSI stands for Small Scale Integration circuits.
(ii) VLSI stands for Very Large Scale Integration circuits.

The fermi-level of intrinsic semiconductor lies mid way between its valence and conduction bands i.e., in the middle of forbidden energy gap of intrinsic semi-conductor.

Note that thermally generated electrons (ni ~10¹⁶m^–3) are negligibly small as compared to those produced by doping.
Therefore, ne \(\approx\) ND
Since n_e n_h = \(n_{i}^{2}\) , The number of holes
n_h = (2.25 x 10³² ) / (5 x10²²)
= ~ 4.5 x 10⁹ m^–3

Conductor

(a) Zener diode.
(b) Helpful and concerned, practical application of theoretical knowledge.

(i) (a) The doping of pure silicon with boron or aluminium will give us \(p-\)type semiconductor 
(b) The doping of pure silicon with arsenic or phosphorous will give us  \(n-\)type semiconductor.
(ii) From the above study, we find that to get better output current ,pure semiconductor has to be adopted with suitable (impurity) atoms.Similarly,in day to day life,the appearence of right kind of persons(leaders) in society can improve their lot.