(a) A photodiode is fabricated by allowing light to fall on a diode through a transparent window. It is fabricated such that the generation of e-n pairs take place near the depletion region.
 

(a) metals, (b) insulators and (c) semiconductors
Two distinguishing features:
(i) In conductors, the valence band and conduction band tend to overlap (or nearly overlap) while in insulators they are separated by a large energy gap and in semiconductors they are separated by a smaJ1'ep.ergygap.  
(ii) The conduction band, of a conductor, has a large number of electrons available for electrical conduction. However the conduction band of insulators is almost empty while that of the semiconductor has only a (very) small number of such electrons available for electrical conduction.

\(9.1\times { 10 }^{ 15 }\)

\(2.25\times { 10 }^{ 6 }m{ s }^{ -1 }\)

\(1.23\times { 10 }^{ 4 }{ s }^{ -1 }\)

(a) For the electron:
Mass m = 9.11 x 10^–31 kg, speed v = 5.4 x 10⁶ m/s. Then, momentum
p = m v = 9.11 x 10^–31 (kg) x 5.4 x 10⁶ (m/s)
p = 4.92 x 10^–24 kg m/s
de Broglie wavelength,\(\lambda\) = h/p
\(=\frac{6.63 \times 10^{-34} \mathrm{Js}}{4.92 \times 10^{-24} \mathrm{~kg} \mathrm{~m} / \mathrm{s}}\)
\(\lambda=0.135 \mathrm{nm}\)
(b) For the ball:
Mass m’ = 0.150 kg, speed v’ = 30.0 m/s.
Then momentum p’ = m’ v ’ = 0.150 (kg) x 30.0 (m/s)
p ’= 4.50 kg m/s
de Broglie wavelength \(\lambda\)’ = h/p’.
\(=\frac{6.63 \times 10^{\pm 34} \mathrm{Js}}{4.50 \times \mathrm{kg} \mathrm{m} / \mathrm{s}}\)
\(\lambda^{\prime}=1.47 \times 10^{-34} \mathrm{~m}\)
The de Broglie wavelength of electron is comparable with X-ray wavelengths. However, for the ball it is about 10^–19 times the size of the proton, quite beyond experimental measurement.

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equal

Circuit diagram of an illuminated photodiode:


Explanation:
The magnitude of the photocurrent depends on the intensity of incident light (photocurrent is proportional to incident light intensity).  Thus photodiode can be used to measure light intensity.

(i) In n-type semiconductor, the semiconductor is doped with pentavalent impurity. The electrons are majority carriers and holes are minority carriers or n_e >> n_h , (n_e = number density of electrons, n_h = number density of holes).
In energy band diagram of n-type semiconductor, the donor energy level E_D is slightly below the bottom of conduction band E_c and thus. the electron can move to conduction band, even with small supply of energy.
  
(ii) In p-type semiconductor, the semiconductor is doped with trivalent impurity. The holes are the majority carriers and electrons are the minority carriers, i.e. n_b >> n_e . In energy band diagram of p-type, the acceptor energy level E_A is slightly above the top of valence band E_V .
Thus, even with small supply of energy, electron from valence band can jump to level E₄ and ionise the acceptor, negatively.

It is the minimum negative potential given to the anode in a photocell for which the photoelectric current becomes zero. If \({ v }_{ 0 }\) is the stopping potential, then maximum K.E. of emitted photoelectron is
\({ \left( K.E \right) }_{ max }={ eV }_{ 0 }=hv-{ \phi }_{ 0 }\)
\(V_{ 0 }=\frac { hv }{ e } -\frac { { \phi }_{ 0 } }{ e } \)
Threshold frequency  It is the minimum frequency of the incident radiation for which just emission of photoelectrons takes place from a metal surface without any K.E. If \(V_{ 0 }\)is the threshold frequency, then using Einstein's photoelectric equation
\(0={ hv }_{ 0 }-{ \phi }_{ 0 }\quad or\quad V_{ 0 }=\frac { { \phi }_{ 0 } }{ h } \)

In photoelectric emission, \(\frac { 1 }{ 2 } { mv }^{ 2 }=hv-{ \phi }_{ 0 }\)
The increase in frequency v of the incident photon. Since the work function \({ \phi }_{ 0 }\)of a given photosensitive surface being fixed, therefore the kinetic energy of the photoelectron increases with increase in the frequency of incident light due to it, the velocity v of photoelectrons increases.

When an electron of mass m is confined to move on a line of length l with velocity v, the de-Broglie wavelength \(\lambda \) associated with electron is  \(\lambda =\frac { h }{ mv } =\frac { h }{ p } \ \ or \ \ p=\frac { h }{ \lambda } =\frac { h }{ { 2l }/{ n } } =\frac { nh }{ 2l } \)
When electron revolves in a circular orbit of radius r; then \(2l=2\pi r\)
\( \ \therefore \ \ p=\frac { nh }{ 2\pi r } \\ \ \ or \ \ p\times r=\frac { nh }{ 2\pi } \)
i.e., angular momentum  \((p\times r)\) of electron is integral multiple of \({ h }/{ 2\pi }\) . This is Bohr's quantization condition of angular momentum.

No, the stopping potential does not depend upon the intensity of incident radiations but depends on the nature of photosensitive surfaces and frequency of the incident radiation.

For a given metal, there exists certain minimum frequency of the incident radiation below which no emission of photoelectrons takes place. This frequency is called threshold frequency. It is a constant quantity for a given metal surface.

\(M a x . K . E .=K_{\max }=e V_0=e \times 1.5 \mathrm{~V}=1.5 \mathrm{eV}\)

\(R=1.097 \times 10^7 \mathrm{~m}^{-1}\)

This model could not explain scattering of \(\alpha\) particle through large angles.

Work function of metal depends upon the amount of restraining forces acting on the electrons to be ejected.In different metals, the amount of restraining forces on the electrons to be ejected is different.Hence, work function for different metals is different.
Here, 
\({ \phi }_{ 0 }=1.2eV=1.2\times 1.6\times { 10 }^{ -19 }J\)
\( As \ { \phi }_{ 0 }=\frac { hc }{ { \lambda }_{ 0 } } \ or \ { \lambda }_{ 0 }=\frac { hc }{ { \phi }_{ 0 } } =\frac { \left( 6.63\times { 10 }^{ -34 } \right) \times \left( 3\times { 10 }^{ 8 } \right) }{ 1.2\times 1.6\times { 10 }^{ -19 } } =1037\times { 10 }^{ -19 }m=1037nm\)
(iii) Work function of metal required to the minimum energy required by an electron to escape from the metal. In day-to-day life, we find that we can purchase something only when we have money, which is at least equal to or more than that price. Thus to purchase comforts of life, we have to work hard and earn money by fair means.

\(Here,\lambda =300nm=300\times { 10 }^{ -9 }m\)
\(=3\times { 10 }^{ -7 }m,{ V }_{ 0 }=0.54V\)
(i) Energy of the incident photon,
\(E=\frac { hc }{ \lambda } =\frac { \left( 6.63\times { 10 }^{ -34 }Js \right) \times \left( 3\times { 10 }^{ 8 }m/s \right) }{ 3\times { 10 }^{ -7 } } =6.63\times { 10 }^{ -19 }J\)
\(=\frac { 6.63\times { 10 }^{ -19 } }{ 1.6\times { 10 }^{ -19 } } eV=4.14eV\)
(ii) Max. K.E. of emitted photoelectron is
\({ K }_{ max }=e{ V }_{ 0 }=e\times 54V=0.54eV\)
(iii) \({ As\ K }_{ max }=\frac { hc }{ \lambda } -{ \phi }_{ 0 }\ or{ \ \phi }_{ 0 }=\frac { hc }{ \lambda } -{ K }_{ max }\)      
\(=4.14eV-0.54eV=3.6eV\)