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Study of Velocity Distribution of Thermionic Electrons with Reference to Triode Valve

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Study of Velocity Distribution of Thermionic Electrons with Reference to Triode Valve Bulletin of Physics Projects, 1, 2016, 33-36 Study of Velocity Distribution of Thermionic electrons with reference to Triode Valve Anupam Bharadwaj, Arunabh Bhattacharyya and Akhil Ch. Das # Department of Physics, B. Borooah College, Ulubari, Guwahati-7, Assam, India # E-mail address: [email protected] Abstract Velocity distribution of the elements of a thermodynamic system at a given temperature is an important phenomenon. This phenomenon is studied critically by several physicists with reference to different physical systems. Most of these studies are carried on with reference to gaseous thermodynamic systems. Basically velocity distribution of gas molecules follows either Maxwell-Boltzmann or Fermi-Dirac or Bose-Einstein Statistics. At the same time thermionic emission is an important phenomenon especially in electronics. Vacuum devices in electronics are based on this phenomenon. Different devices with different techniques use this phenomenon for their working. Keeping all these in mind we decided to study the velocity distribution of the thermionic electrons emitted by the cathode of a triode valve. From our work we have found the velocity distribution of the thermionic electrons to be Maxwellian. 1. Introduction process of electron emission by the process of increase of Metals especially conductors have large number of temperature of a metal is called thermionic emission. The free electrons which are basically valence electrons. amount of thermal energy given to the free electrons is Though they are called free electrons, at room temperature used up in two ways- (i) to overcome the surface barrier (around 300K) they are free only to move inside the metal and (ii) to give a velocity (kinetic energy) to the emitted with random velocities. Because, when they reach the electrons. The velocities so acquired by the emitted metal surface in course of their random motion and try to electrons vary in magnitude and direction. In our leave the surface an attractive force comes into existence investigation we try to have an overview of the velocity which prevents them from leaving the surface. Thus they distribution of the thermionic electrons. have to do an amount of work against this attractive force 1.1. Theory: to come out from the metal surface. The minimum energy The free electrons in a metal move in a potential field required to do this amount of work to overcome this which can be approximated as shown in the following opposition is called work function of the metal. Work figure. The maximum energy possessed by an electron at function is a temperature dependent quantity. This extra 0K is called Fermi energy EF. All the energy states below energy required by the free electrons to come out from the EF are filled up and all the states above it are empty. If E0 metal surface can be supplied by different means. One of be the height of the surface potential energy barrier then these means is to increase the thermal energy of the free E0- EF is the minimum energy at 0K that enables an electrons by increasing the temperature of the metal. The electron to escape from the metal. This is known as the 33 Bulletin of Physics Projects, 1, 2016, 33-36 work function of the metal. If ɸ be the voltage equivalent where L is the axial length of the electrodes, is the of work function then- radius of the anode and is a function of (where r is k ………………………………….(1) Obviously no electron emission is possible at 0K. the radius of the cathode); its value may be taken as 1 However, if temperature of metal is increased then when is large. In deriving above relation the electrons some of electrons may be excited to higher states having are assumed to start with zero velocity from the cathode. energy greater than E0 and can escape from the metal Eq. (3) is known as Child-Langmuir law under space surface. Using Fermi–Dirac statistics it is possible to charge limited condition [2]. calculate the number of electrons which are emitted from Thus According to Child-Langmuir law the space the metal surface per sec per unit area with energies charge limited condition the plate current in a vacuum exceeding E0 at a particular temperature of the metal tube is related to the plate voltage by the relation: (cathode). The expression for thermionic emission current density (J) is found to be- = K ……………………………………….(4) ……………………………(2) where K = is a constant for a given tube. where, A is a constant independent of the metal, T is the temperature of the metal in Kelvin, eɸ is the work function Now if we apply a negative grid voltage Vg, then of the metal and k is the Boltzmann constant. Above electrons having kinetic energy less than eVg will be relation was first derived thermodynamically by obstructed by the grid from reaching the plate. As a result Richardson and Dushman and is therefore known as the plate current Ip will decrease by an amount determined Richardson-Dushman’s equation [1]. by the relation: 1.2. Working Principle: ……………………………………(5) In our experiment we use a vacuum triode having ………………………………………...(6) concentric cylindrical electrodes- namely (i) indirectly Thus, the velocity v of the obstructed electrons is heated cathode, (ii) grid and (iii) anode or plate as shown in the Fig. 1 and Fig. 2 [1]. determined by Vg and is determined by the decrease in plate current (Ip0-Ip1). In this way if we increase the value of negative grid voltage Vg step by step, electrons having higher and higher velocities will be obstructed and from the difference of successive plate currents we can have the number of electrons obstructed having different velocities. From these data we can draw a graph relating velocities distribution of thermionic electrons. 2. Experimental Details The circuit arrangement for the above mentioned Fig. 1: Internal structure of a cylindrical triode valve experiment is shown in the Fig. 3. Fig. 2: Symbolic diagram of a triode valve Fig. 3: Circuit diagram of the experimental set-up Using cylindrical coordinates and making a rigorous 3. Results and Discussions treatment it can be shown that plate current for such a Data were collected for the Plate Current (I ), and triode for zero grid voltage is given by: p difference in plate current (ΔIp) for different grid Voltages (V ), at constant Plate Voltage (V ) and the process was g p = ……………………………….. (3) repeated for different set of constant Plate Voltages (Vp) of 100 volts, 125 volts, 150 volts, 200 volts and 225 volts. 34 Bulletin of Physics Projects, 1, 2016, 33-36 Fig 4: Variation of Ip as a function of Vg for different values of plate voltages Vp (a) 150 V, (b) 200 V, (c) 225 V and (d) 250 V 35 Bulletin of Physics Projects, 1, 2016, 33-36 The data were then plotted between the difference in plate In spite of all these effects and simplicity of the current (ΔIp) and grid Voltage (Vg), at a constant Plate experiment the result obtained is found to be in agreement Voltage (Vp) using MATLAB software and are shown in with theoretical concept regarding velocity distribution of the Fig. 4 (a-d). Gaussian curve fitting done using the thermionic electrons. MATLAB software are also shown for each plot. 5. Acknowledgement 4. Conclusions This project was carried out as part of the Physics From the graphs drawn using the data recorded from Major Course during 6th semester 2015 based on the new the above experiment the velocity distribution of the syllabus of the Gauhati University for undergraduate level thermionic electrons of a triode valve is found to be under the supervision of Dr. Akhil Chandra Das, Associate Maxwellian. There are several picks on each graph. These Professor, Department of Physics, B Borooah College, picks may be attributed to various causes like (i) secondary Guwahati-781007. We express our gratitude to our emission of electrons due to collision of the electrons with respected teachers for their help during the investigation. atoms on the surface of the plate, (ii) formation of layers 6. References by the emitted electrons near the cathode and collision [1] http://www.wikipedia.com. among the emitted electrons. Even there may be reflection [2] Undergraduate level Books on electronics and statistical effect due to the layer formation by the emitted electrons. mechanics. 36 .
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