Discovery of Electrons PDF

Discovery of electrons The first evidence to establish the existence of electrons was provided by J.J. Thomson's experiment in the 1897 or late 18's, where he measured the speed and the charge-to-mass ratio ( e/m), called the SPECIFIC CHARGE, of cathode ray...

Discovery of electrons The first evidence to establish the existence of electrons was provided by J.J. Thomson's experiment in the 1897 or late 18's, where he measured the speed and the charge-to-mass ratio ( e/m), called the SPECIFIC CHARGE, of cathode rays. The fact that cathode rays we're not electromagnetic waves was based on the following 1. The speeds were typically one-tenth that of light 2. They could be deflected by electric and magnetic fields. The value of e/m obtained by Thomson was always the same despite the source or method of production of the cathode rays. This suggested that electrons are all alike and that are a universal constituent of matter. Thompson estimated the mass(m) of an electron, knowing e/m. Using modern values m is 9.11×10^15kg. i.e it's 1837 times smaller than the mass of the hydrogen atom. In most cases, the electron can be regarded as a sub-atomic the particle with a negative charge of value e, the electronic charge and a very small mass. The value of the mass quoted above is known as the "REST MASS" and it can be measured directly. Ordinary particles are characterized by size and shape but such properties can't be stated precisely for subatomic particles SPEED OF AN ELECTRON Consider an electron of mass m and and charge e emitted from a hot cathode and accelerated by an electric field towards the anode, it experiences a force due to the electric field and work is done on it. The system loses electric potential energy while the electron gains kinetic energy. If the pd V between the cathode and anode responsible for the field and the electron starts from rest and moves in a vacuum obtaining speed u as it reaches the anode, By principal of conservation of energy Electrical work done on the electron =kinetic energy gained by the electron, Work done =VIt Ke=½mu² But Q=It Hence QV=½mu² But for an electron Q=e eV=½mu² Hence u=√(2eV/m) DEFLECTION OF ELECTRONS IN A MAGNETIC FIELD When electrons move through a magnetic field, it experiences a force perpendicular to its direction of motion and the magnetic field. This force causes the electron to deflect from its original path. The value of the force acting remains the same (Bev) and since the direction of motion and magnetic field are mutually perpendicular, the force so perpendicular to the new direction. The force therefore changes direction but not speed of the electrons Therefore, an electron of mass m describes a circular arc of radius r,the constant radial force (Bev) is the centripetal force and so Bev=mv2/r This equation describes the path of an electron in a magnetic field DENFITION OF SPECIFIC CHARGE OF THE ELECTRONS Specific charge is the ratio of charge of a particle to its mass SPECIFIC CHARGE OF AN ELECTION. This is the value or quantity that can be worked out for any particle that has ; 1.mass(m) 2.electron charge(e) Specific charge =Charge that a particle has/mass Therefore it’s the ratio of charge to mass It MUST be measured in (C/kg) Example. 1.Find the specific charge of an electron. Charge =-1.60*10^-19C Mass=9.11*10^-31 kg e/m=-1.60*10^-19/9.11*10^-31 = -1.76*10^11C/kg Thermionic emission is the release of electrons from a heated metal surface Applications Vacuum tubes Cathode rays X-tray tube  RICHARDSONS EQUATION Richardson’s equation, also known as the Richardson-Dushman equation, describes the current density of thermionic emission from a heated surface. The equation is given by: J=AT2exp(kT−W ) where: ( J ) is the current density, ( A ) is Richardson’s constant, ( T ) is the absolute temperature, ( W ) is the work function of the material, ( k ) is the Boltzmann constant12. This equation is crucial in understanding the behavior of electrons emitted from hot surfaces, which is important in various applications like vacuum tubes and electron microscopes. WORK FUNCTION Work function is the minimum amount of energy required by an electron to escape from a metal surface. THERMIONIC DIODE This is an electronic device that uses the principle of thermionic emission to allow current flow in one direction (Action) The cathode and anode are mounted in the evacuated glass bulb, when the cathode is heated by DC electrons are suppled by thermionic emission Current flows in a circuit. If the anode is made positive with respect to the cathode , cathode electrons are repelled by the anode and no current flows Construction It includes two electrodes an anode and a cathode where the cathode generates the free electrons into the vacuum whereas the anode collects free electrons from the cathode. So free electrons will leave the cathode to enter the anode. These two electrodes are enclosed within an empty envelope of glass.  The anode terminal is a hollow cylinder and the material used to make this terminal is nickel or molybdenum. The cathode terminal is a nickel cylinder covered with barium oxide & strontium. Here, the anode terminal is surrounded by the cathode. An empty space is present in between the two electrodes through which the electric current flows. In a vacuum tube, the anode terminal is larger as compared to the cathode to dissipate heat without an extreme increase in temperature. Generally, cooling fins are arranged with an anode to remove the generated heat at the anode. X-tics of Thermionic Diode 1. Unidirectional current flow: Allows current to flow in one direction, from cathode to anode, but blocks it in the reverse direction. 2. Non-linear current-voltage relationship: The current through the diode is not directly proportional to the applied voltage. 3. Threshold voltage: A minimum voltage (around 0.5-1.5V) is required to initiate current flow. 4. Saturation current: Beyond a certain voltage, the current reaches a maximum value and remains constant. 5. Temperature dependence: Emission of electrons from the cathode depends on temperature 6. High voltage drop: Typically around 100-200V is required to achieve significant current flow. 7. Low current density: Compared to modern semiconductor diodes, thermionic diodes have relatively low current density. 8. Slow switching times: Due to the physical process of electron emission and transport. 9. Relatively high power consumption: Due to heating the cathode and maintaining the vacuum. 10. Fragile and bulky: Glass or metal tubes are used, making them more fragile and larger than semiconductor diodes. These characteristics made thermionic diodes suitable for early applications like radio amplification and rectification but have largely been replaced by semiconductor diodes in modern electronics. THREE HALVES POWER Known as child Langmuir law or child's law Describes the maximum space - charge. Limited current in a planar vacuum diode / plamordiode of infinity radius radius as a function of the anode - cathood potential difference and separation distance expressed by; J=KVd2/3 J- current density A/msq Vd- potential difference between anode and cathode ( V) d- distance between anode and cathode exponent 3/2(m) k-constant Law derived under the following assumption -Electrons travel ballistically between electrodes ( no scattering) -space charge of ions is negligible in the interele ctrode region -Electrons have zero initial velocity at the cathode surface. NB: Child's law is valid in the vacuum regime Practical application vacuum tubes and electron guns -it's used to design the electrodes and operating voyages to achieve the desired electron beam properties -Plasma sheath Governs the formation of plasma sheath at the boundary between a plasma and a solid surface. (determines sheath thickness and potential drop) -Particle accelerators Used to design the electron on that produce the initial electron beam. CATHODE RAYS Cathode rays are streams of fast-moving electrons emitted from the cathode right. Properties of Cathode Rays They travel from the cathode to the anode in a straight line They are electrons and carry a negative charge They can be deflected in both electric and magnetic fields They cause fluorescence Motion of cathode rays. A cathode rays are streams of electrons emitted from the cathode into a vacuum tube. They experience different motion when subjected to electric and magnetic fields. Their behavior in these fields is governed by the forces exerted on them Motion in electric field As cathode rays are negatively charged, they experience force in a negative direction of the electric field. F= -eE. Where F is the force, e is the charge(-ve) and E is the electric field From Newton's law of motion, F=ma, ma=-eE , a=-eE/m This can be used to calculate the acceleration of the cathode rays. Acceleration and trajectory. Electrons in a magnetic field undergo uniform acceleration. Their velocity changes according to the equation. v= u - (eE/m)t If the electrons initially move parallel to the field, they will accelerate along the direction of the field. If the electrons move perpendicular to the field force, they will follow a parabolic trajectory. Motion in magnetic field. A charged particle moving with velocity (v) in a magnetic field (B) experiences a magnetic force (F). Through the magnetic field, the particles are deflected upwards or downwards depending on the direction of the magnetic field. If the magnetic field has a component perpendicular to the direction of the velocity, then there will be a force with a perpendicular component to the direction of the velocity.This force is referred to as Lorentz force. F=-evB. Where V is the velocity,e is charge and B is the magnetic field. Circular motion. Because the force is always perpendicular to the velocity, the electrons speed remains constant but the direction changes causing them to move in circular or helical paths. If the velocity of the electrons is perpendicular to the magnetic field, it will move in circular paths with a given radius. The radius can be calculated from, F=mv²/r  mv²/r=evB r=mv/eB If the velocity has a component along the magnetic field, the motion will be helical (spiral). Cyclotron frequency. This is the frequency at which the electro revolves around the magnetic field lines.