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Transcript
Measurement of Charge to Mass Ratio For an Electron ( Thompson’s Experiment ) Carleton University The scale of the subatomic world You and me Insect Virus on an insect 1m 10-3 m Atom of a virus 10-6 m Proton 10-9 m + electron 10-12 m Carleton University 10-15 m Quark The Electron: • is an elementary particle: smallest speck of matter • is normally found in the immediate vicinity of a nucleus, forming an atom • Mass (me): 9.11 x 10-31 kg • Charge (e): 1.6 x 10-19 C (C = Coulombs) • Charge is found by Millikan’s Oil Drop experiment • So, if we can find e/me, we can determine me • In 1897, J.J. Thompson found this value • Ratio (e/me): -1.76 x 1011 C/kg • Your Job: try to repeat that measurement today Carleton University 3 Forces affecting the electron: 1. The electric field: E e- the electric field, E, produces a force FE = q·E (q = e, the charge of the electron) The electric field, E, always points in the direction that a +ve charge would move if it were within the field. Carleton University 4 Forces affecting the electron: 2. The magnetic field: Bout e- The magnetic field (Bout) produces a force: FB = Bout·e·v (v is the velocity of the electron) This force is perpendicular to both Bout and v. Carleton University Into the page Out of the page 5 Finding e/m: • Electrons move in circles in magnetic fields • This motion produces a centripetal force mv 2 F R • We can equate this to FB: mv 2 Bev R • Re-arranging: e v m BR e- v Bout R • Thus, to find e/m we need to know 3 things: the magnetic field, B, the radius of curvature, R, and the velocity of the electrons, v. Carleton University 6 Finding the magnetic field, B: • “Helmholtz” coil arrangement delivers uniform magnetic field B Beckman “Lambda” I D.C. Power Supply • B depends on current, and is calibrated to be: B = I x 4.23 x 10-3 Wb m-2 (I measured in Amps) Carleton University 7 Determine the radius, R: 4 • Measure y - deflection at a distance, x, from the exit of the electron (x,y) = (4,-2) •Given (x,y) - find R x y R 2y 2 R 2 Ry y R x x2 y2 R 2y Carleton University 2 2 2 2 1 y x R 2 •To prove this, try Pythagoras: ( R y) 2 b2 ( R 2 x 2 ) 2 3 x R y b=R-y 8 Determine the velocity, v: • Now switch on the Electric Field • Use it to cancel the effects of the B field V V E d 0.052 • Use the Electric field to cancel the deflection at the x value where the magnetic deflection was measured Ee Bev Carleton University E v B (m / s) +ve d 8 7 6 5 4 3 2 1 2 1 -1 -2 -ve CENCO D.C. Power Supply Voltage (5kV) 9 E Procedure: • Plug in transformer for cathode heater supply • Switch on CENCO D.C. supply to accelerate electrons down the tube and onto the screen set to ~ 2400 V • There should now be a blue trace on the screen • Switch on Beckman meter and Lambda power supply unit connected to coils set to ~ 0.2 A • Determine B Carleton University 10 Procedure: • Measure (x,y): determine R •Switch on second CENCO DC supply connected to electrodes on top of mica screen set to ~ 1.5 kV • Adjust to cancel deflection: determine v • Fill in worksheet and calculate e/m • Switch off all power supplies Carleton University 11 Thompson's e/m experiment Your Measurements Units Units R = (x 2 + y 2 ) / 2y metres amps B= 4.23x10 -3 I Tesla volts E = V / 0.052 volts/metre v=E/B metres/sec e/m = v / B R Coulombs/kg metres Radius(R) of the track x y Determining the I V Determining the Calculated quantities metres Magnetic Field (B) Determining the Electric Field (E) Determining the electron's velocity(v) Determining e / m Carleton University