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There are two theories of catalysis which is described as follows. (1) Intermediate compound theory (i) This theory was proposed by Clement and Desormes in 1806. According to this theory, the desired reaction is brought about by a path involving the formation of an unstable intermediate compound, followed by its decomposition into the desired end products with the regeneration of the catalyst. (ii) The intermediate compund may be formed in either of two ways (a) When the intermediate compound is reactive and reacts with the other reactants. \[AB+X\underset{\text{intermediate}}{\mathop{\to \,\,BX\,\,\,+}}\,A\] \[BX+C\to CB+X\]                                                        .....(i)           (b) When the intermediate is unstable and decomposes to give the final product. \[A+B+X\underset{\text{intermediate}}{\mathop{\to ABX\to }}\,AB+X\]                                                .....(ii)      Where, A, B and C are the reactant molecules and X is the molecule of the catalyst. The first type of reaction sums up to,  \[AB+C\to CB+A\] While the second to, \[A+B\to AB\] in many cases, the intermediate compounds postulated to be formed are known compounds and often their presence is detected. (2) Adsorption theory (i) This theory is applicable to reactions between gases in the presence of a solid catalyst. Some typical examples are as follows. (ii) The contact process for the oxidation of \[S{{O}_{2}}\] to \[S{{O}_{3}}\] with atmospheric oxygen in the presence of platinum as the catalyst. (iii) The Haber's process for the synthesis of ammonia with iron as the catalyst. (iv) Adsorption results in the loosening of the chemical bonds in the reactant molecules, so that their rupture becomes easier. This is confirmed by the observed lower activation energies for heterogeneous catalytic reactions in the presence of the catalysts as compared to that for the same reaction in the absence of the catalyst.

(1) Purification of water by alum (coagulation) : Alum which yield \[A{{l}^{3+}}\]ions, is added to water to coagulate the negatively charged clay particles. (2) In rubber and tanning industry (coagulation and mutual coagulation) : Several industrial processes such as rubber plating, chrome tanning, dyeing, lubrication etc are of colloidal nature (i) In rubber platting, the negatively charged particles of rubber (latex) are made to deposit on the wires or handle of various tools by means of electrophoresis. The article on which rubber is to be deposited is made anode. (ii) In tanning the positively charged colloidal particles of hides and leather are coagulated by impregnating, them in negatively charged tanning materials (present in the barks of trees). Among the tanning agent chromium salts are most commonly used for the coagulation of the hide material and the process is called chrome tanning. (3) Artificial rains : It is possible to cause artificial rain by throwing the electrified sand or silver iodide from an aeroplane and thus coagulating the mist hanging in air. (4) Smoke precipitation (Coagulation) : Smoke is a negative sol consisting of carbon particles dispersed in air. Thus, these particles are removed by passing through a chamber provided with highly positively charged metallic knob. (5) Formation of deltas (coagulation) : River water consists of negatively charged clay particles of colloidal dimension. When the river falls into the sea, the clay particles are coagulated by the positive \[N{{a}^{+}},\,{{K}^{+}},\,M{{g}^{2+}}\] ions etc. present in sea water and new lands called deltas are formed. (6) Clot formation : Blood consists of negatively charged colloidal particles (albuminoid substance). The colloidal nature of blood explains why bleeding stops by applying a ferric chloride solution to the wound. Actually ferric chloride solution causes coagulation of blood to form a clot which stops further bleeding. (7) Colloidal medicine : Argyrol and protargyrol are colloidal solution of silver and are used as eye lotions colloidal sulphur is used as disinfectant colloidal gold, calcium and iron are used as tonics. (8) Coating of Photographic plates : These are thin glass plates coated with gelatin containing a fine suspension of silver bromide. The particles of silver bromide are colloidal in nature.     

(1) Conducting rod : A conducting rod of length \[l\] whose one end is fixed, is rotated about the axis passing through it's fixed end and perpendicular to it's length with constant angular velocity \[\omega \]. Magnetic field (B) is perpendicular to the plane of the paper. emf induces across the ends of the rod where \[v=\]  frequency (revolution per sec) and T = Time period. (2) Cycle wheel : A conducting wheel each spoke of length \[l\] is rotating with angular velocity \[\omega \] in a given magnetic field as shown below in fig. Due to flux cutting each metal spoke becomes identical cell of emf e (say), all such identical cells connected in parallel fashion \[{{e}_{net}}=e\] (emf of single cell). Let N be the number of spokes hence \[{{e}_{net}}=\frac{1}{2}Bw{{l}^{2}};\,\omega =2\pi \nu \]  Here  \[{{e}_{net}}\propto {{N}^{o}}\] i.e. total  emf does not depends on number of spokes 'N'. (3) Faraday copper disc generator : A metal disc can be assumed to made of uncountable radial conductors when metal disc rotates in transverse magnetic field these radial conductors cuts away magnetic field lines and because of this flux cutting all becomes identical cells each of emf 'e' where \[e=\frac{1}{2}B\omega {{r}^{2}},\] (4) Semicircular conducting loop : If a semi-circular conducting loop (ACD) of radius 'r' with centre at O, the plane of loop being in the plane of paper. The loop is now made to rotate with a constant angular velocity \[\omega \], about an axis passing through O and perpendicular to the plane of paper. The effective resistance of the loop is R. In time t the area swept by the loop in the field i.e. region II   \[A=\frac{1}{2}r(r\theta )=\frac{1}{2}{{r}^{2}}\omega \,t\];  \[\frac{dA}{dt}=\frac{{{r}^{2}}\omega }{2}\] Flux link with the rotating loop at time t  \[\varphi =BA\] Hence induced emf in the loop in magnitude \[|e|=\frac{d\varphi }{dt}=B\frac{dA}{dt}=\frac{B\omega {{r}^{2}}}{2}\] and induced current  \[i=\frac{|e|}{R}=\frac{B\omega {{r}^{2}}}{2R}\]  

Amplifier is a device by which the amplitude of variation of ac signal voltage / current/ power can be increased (1) The signal to be amplified \[({{V}_{i}})\] is applied in the grid circuit and amplified output is obtained from the plate circuit     (2) The voltage at grid is the sum of signal \[{{V}_{i}}\] and grid bias \[{{V}_{gg}}\]. \[{{V}_{g}}={{V}_{gg}}+{{V}_{i}}\] (3) Small change in grid voltage results in a large change in plate current so results in a large change in voltage across \[{{R}_{L}}\,({{V}_{0}}={{i}_{p}}{{R}_{L}}\,\Rightarrow \,\Delta {{V}_{0}}=\Delta {{i}_{p}}{{R}_{L}})\] (4) The linear portion of the mutual characteristic with maximum slope is chosen for amplification without distortion.   (i) For the positive half cycle of input voltage \[({{V}_{i}})\] : \[{{V}_{g}}\] becomes less negative, so \[{{i}_{p}}\] increases (ii) For the negative half cycle of input voltage \[({{V}_{i}})\] : \[{{V}_{g}}\] becomes more negative, so \[{{i}_{p}}\] decreases (iii) The phase difference between the output signal and input signal is \[{{180}^{o}}\] (or \[\pi \])   (5) Voltage amplification   Current through the load resistance is given by \[{{i}_{p}}=-\frac{\mu {{V}_{i}}}{{{r}_{p}}+{{R}_{L}}}\,\] \[\Rightarrow \,{{V}_{0}}={{i}_{p}}{{R}_{L}}=\frac{-\,\mu {{V}_{i}}{{R}_{L}}}{{{r}_{p}}+{{R}_{L}}}\]  \[\Rightarrow \] Voltage gain \[=\frac{{{V}_{0}}}{{{V}_{i}}}=-\frac{\mu {{R}_{L}}}{{{r}_{p}}+{{R}_{L}}}\] Numerically \[A=\frac{\mu {{R}_{L}}}{{{r}_{p}}+{{R}_{L}}}=\frac{\mu }{1+\frac{{{r}_{p}}}{{{R}_{L}}}}\] (i) If \[{{R}_{L}}=\,\,\infty \,\,\Rightarrow A\] will be maximum and \[{{A}_{\max }}=\mu \] (Practically \[A<\mu \]) (ii) If \[{{r}_{p}}={{R}_{L}}\Rightarrow A=\frac{\mu }{2}\] (iii) Power at load resistance \[P={{i}_{p}}{{V}_{0}}=i_{p}^{2}{{R}_{L}}\] Condition for maximum power \[{{R}_{L}}={{r}_{p}}\] \[\therefore \] \[{{P}_{\max }}={{\left( \frac{\mu {{V}_{i}}}{{{R}_{L}}+{{R}_{L}}} \right)}^{2}}\times {{R}_{L}}=\frac{{{\mu }^{2}}V_{i}^{2}}{4{{R}_{L}}}\]

(1) Plate or dynamic resistance \[({{r}_{P}})\] (i) The slope of plate characteristic curve is equal to \[\frac{1}{\text{plate}\,\text{resistance}}\] or It is the ratio of small change in plate voltage to the change in plate current produced by it, the grid voltage remaining constant. That is, \[{{r}_{p}}=\frac{\Delta {{V}_{\text{p}}}}{\Delta {{i}_{p}}},{{V}_{G}}=\text{constant}\].     (ii) It is expressed in kilo ohms \[(K\Omega )\]. Typically, it ranges from \[8K\Omega \] to\[40K\Omega \]. The \[{{r}_{P}}\] can be determined from plate characteristics. It represents the reciprocal of the slope of the plate characteristic curve. (iii) If the distance between plate and cathode is increased the \[{{r}_{P}}\] increases. The value of \[{{r}_{P}}\] is infinity in the state of cut off bias or saturation state.   (2) Mutual conductance (or trans conductance) \[({{g}_{m}})\] (i) It is defined as the ratio of small change in plate current \[(\Delta {{i}_{p}})\] to the corresponding small change in grid potential \[(\Delta {{V}_{g}})\] when plate potential \[{{V}_{p}}\] is kept constant i.e. \[{{g}_{m}}={{\left( \frac{\Delta {{i}_{p}}}{\Delta {{V}_{g}}} \right)}_{{{V}_{p\,}}\text{is}\,\text{constant}}}\]   (ii) The value of \[{{g}_{m}}\] is equal to the slope of mutual characteristics of triode. (iii) The value of \[{{g}_{m}}\] depends upon the separation between grid and cathode. The smaller is this separation, the larger is the value of \[{{g}_{m}}\] and vice versa. (iv) In the saturation state, the value of \[\Delta {{i}_{p}}=0\], \[{{g}_{m}}=0\]   (3) Amplification factor \[(\mu )\] : It is defined as the ratio of change in plate potential \[(\Delta {{V}_{p}})\] to produce certain change in plate current \[(\Delta {{i}_{p}})\] to the change in grid potential \[(\Delta {{V}_{g}})\] for the same change in plate current \[(\Delta {{i}_{p}})\]i.e. \[\mu =-\,{{\left( \frac{\Delta {{V}_{p}}}{\Delta {{V}_{g}}} \right)}_{\Delta {{I}_{p}}=\,\text{a constant }}}\]; negative sign indicates that \[{{V}_{p}}\] and \[{{V}_{g}}\] are in opposite phase. (i) Amplification factor depends upon the distance between plate and cathode \[({{d}_{pk}}),\] plate and grid \[{{d}_{pg}}\] and grid and cathode \[({{d}_{gk}})\]. i.e. \[\mu \,\propto \,{{d}_{pg}}\propto \,{{d}_{pk}}\propto \frac{1}{{{d}_{gk}}}\] (ii) The value of \[\mu \] is greater than one. (iii) Amplification factor is unitless and dimensionless.   (4) Relation between triode constants : The triode constants are not independent of each other. They are related by the relation \[\mu ={{r}_{p}}\times {{g}_{m}}\] The \[{{r}_{p}}\] and \[{{g}_{m}}\] depends on \[{{i}_{p}}\] in the following manner \[{{r}_{p}}\propto {{i}_{p}}^{-1/3}\], \[{{g}_{m}}\propto {{i}_{p}}^{1/3}\], \[\mu \] does not depend on \[{{i}_{p}}\]. Above three constants may be determined from any one set of characteristic curves.   \[{{r}_{p}}=\frac{{{V}_{P1}}-{{V}_{P2}}}{{{I}_{PA}}-{{I}_{PB}}}\], \[{{g}_{m}}=\frac{{{I}_{PA}}-{{I}_{PB}}}{{{V}_{G1}}-{{V}_{G2}}}\], \[\mu =-\frac{{{V}_{P1}}-{{V}_{P2}}}{{{V}_{G2}}-{{V}_{G1}}}\]

A graph represents the variation of \[{{i}_{p}}\] with \[{{V}_{p}}\] at a given filament current \[({{i}_{f}})\] is known as characteristic curve. The curve is not linear hence diode valve is a non-ohmic device. (1) Space charge limited region (SCLR) : In this region current is space charge limited current. Also \[{{i}_{p}}\,\propto \,V_{p}^{3/2}\]\[\Rightarrow \]\[{{i}_{p}}=kV_{p}^{3/2}\]; where k is a constant depending on metal as well as on the shape and area of the cathode. This is called child?s law. (2) Linear region (LR) : In this region \[{{i}_{p}}\,\propto \,{{V}_{p}}\] (3) Saturated region (SR) or temperature limited region (TLR) : In this part, the current is independent of potential difference applied between the cathode and anode. \[{{i}_{p}}\ne f({{V}_{p}})\], \[{{i}_{p}}=f\] (Temperature) The saturation current follows Richardson Dushman equation i.e. \[i=AS{{T}^{2}}{{e}^{-{{\varphi }_{0}}/kT}}\];  Here A = Emission constant =\[\frac{4\pi \ me{{k}^{2}}}{{{h}^{3}}}amp/{{m}^{2}}-{{k}^{2}}\] S = Area of emitter in \[{{m}^{2}}\];  T = Absolute temperature in K \[{{\varphi }_{0}}\]= Work function of metal in Joule; k =Boltzmann constant   The small increase in \[{{i}_{p}}\] after saturation stage due to field emission is known as Shottkey effect. (4) Diode resistance (i) Static plate resistance or dc plate resistance : \[{{R}_{p}}=\frac{{{V}_{p}}}{{{i}_{p}}}\]. (ii) Dynamic or ac plate resistance : If at constant filament current, a small change \[\Delta {{V}_{P}}\] in the plate potential produces a small change \[\Delta {{i}_{p}}\] in the plate current, then the ratio \[\Delta {{V}_{p}}/\Delta {{i}_{p}}\] is called the dynamic resistance, or the 'plate resistance' of the diode \[{{r}_{p}}=\frac{\Delta {{V}_{p}}}{\Delta {{i}_{p}}}\]. (iii) In SCLR : \[{{r}_{p}}<{{R}_{p}}\],        (iv) In TLR  :\[{{R}_{p}}<{{r}_{p}}\] and \[{{r}_{p}}=\infty \]. (5) Uses of diode valve (i) As a rectifier (ii) As a detector (iii) As a transmitter                        (iv) As a modulator  

  (1) Inventor : Fleming (2) Principle : Thermionic emission (3) Number of electrodes : Two (4) Working : When plate potential \[({{V}_{p}})\] is positive, plate current\[({{i}_{p}})\] flows in the circuit (because some emitted  electrons reaches to plate). If \[+{{V}_{p}}\] increases \[{{i}_{p}}\] also increases and finally becomes maximum (saturation).     (5) Space charge : If \[{{V}_{p}}\]is zero or negative, then electrons collect around the plate as a cloud which is called space charge. space charge decreases the emission of electrons from the cathode.

(1) Those tubes in which electrons flows in vacuum are called vacuum tubes. (2) These are also called valves because current flow in them is unidirectional. (3) Vacuum in vacuum tubes prevents the emission of secondary electrons and burning of heated filament (which will happen if we use air in place of vacuum) (4) Every vacuum tube necessarily contains two electrodes out of which one is always electron emitter (cathode) and another one is electron collector (anode or plate). (5) Depending upon the number of electrodes used the vacuum tubes are named as diode, triode, tetrode, pentode.... respectively, if the number of electrodes used are 2, 3, 4, 5..... respectively.  

(1) The phenomenon of ejection of electrons from a metal surface by the application of heat is called thermionic emission and emitted electrons are called thermions and current flowing is called thermion current. (2) Thermions have different velocities. (3) This was discovered by Edison (4) Richardson - Dushman equation for current density (i.e. electric current emitted per unit area of metal surface) is given as \[J=A{{T}^{2}}{{e}^{-\,{{W}_{0}}/kT}}=A{{T}^{2}}{{e}^{-\frac{qV}{kT}}}=A{{T}^{2}}{{e}^{-\,\,\frac{11600V}{T}}}\] where A = emission constant \[=12\times {{10}^{4}}\] amp/ \[{{m}^{2}}-{{K}^{2}}\], k = Boltzmann?s constant, T = Absolute temp and \[{{W}_{0}}=\] work function.   (5) The number of thermions emitted per second per unit area (J) depends upon following : (i) \[J\propto {{T}^{2}}\]  (ii) \[J\propto {{e}^{-{{W}_{0}}}}\] Types of thermionic emitters  

Directly heated emitter	Indirectly heated emitter
Cathode is directly heated by passing current.	Cathode is indirectly heated.
Thermionic current is less.	Thermionic current is more.
Energy consumption and life is small.	Energy consumption and life is more.

 

(1) Free electron in metal experiences a barrier on surface due to attractive Coulombian force. (2) When kinetic energy of electron becomes greater than barrier potential energy (or binding energy\[{{E}_{b}}\]) then electron can come out of the surface of metal. (3) Fermi energy \[({{E}_{f}})\]: Is the maximum possible energy possessed by free electron in metal at 0K temperature (i) In this energy level, probability of finding electron is 50%. (ii) This is a reference level and it is different for different metals. (4) Threshold energy (or work function \[{{W}_{0}}\]) : Is the minimum energy required to take out an electron from the surface of metal. Also \[{{W}_{0}}={{E}_{b}}{{E}_{f}}\]     Work function for different materials \[{{({{W}_{0}})}_{\text{Pure tungsten}}}\text{ }\!\!~\!\!\text{ }~=\text{ }4.5eV\] \[{{({{W}_{0}})}_{\text{Throated tungsten}}}~=\text{ }2.6eV\] \[{{({{W}_{0}})}_{\text{Oxide coated tungsten}}}=\text{ }1eV\]   (5) Four processes of electron emission from a metal are (i) Thermionic emission         (ii) Photoelectric emission  (iii) Field emission  (iv) Secondary emission