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The Mass Spectrometer In the first part of this experiment you will "weigh the electron" by observing an electron beam as itis being deflected by a magnetic field. Equipment List: Tel- Atomic model 525 deflection tube and stand 2 Tel. Atomic model 813 adjustable high voltage power supplies High Voltage Leads - pair of Tel-Atomic model 502 Helmholtz coils to produce Magnetic Field A low voltage power supply to supply the current to the coils A DMM to measure the current Leads for connections to the Helmholtz coils Apparatus Notes: The Deflection Tube that you will use in this experiment the same deflection tabe that you usedi the Electrostatic Deflection experiment This acceleration voltageresults in: change in the kinetic energy of the electrons, allowing usto calculate the horizontal speed of the electrons by (1) A slit placed after the anode canses the electron beam to assume its characteristic shape asit enters the spherical portion of the tube. In that part of the tube. the electrons eventually strikea luminescent screea so we can measure its deflection The Helmholtz Coils are simply two identical coils that are separated by distance equal to their radius. Such an arrangement of coils known to produce very uniform magnetic field around the midpoint between the two coils. (For the details, see problem 61 chapter 28.) At the midpoint between the coils. the magnitude of the magnetic fieldis given by: (2) R,125 In the above equation the permeability of free space (vacuum) 4m x 10 T-m/A. Nis the number turns in each coil (320), lis the current in each turn. and Ris the radius of each coil (0,068 m). "Weighing the Electron " As discussed in your text book, when an electron with velocity v eaters uniform magnetic field B at right angle to the field. the electron will move in circle with aradius eB (3) Combining this with cq. 1. wecan solve for the mass of the electron eB'r 2V. (4) So, to determine the mass of the election, we need to determine B. and V. We control the acceleration voltage. (V.) one of the power supplies so that easy. We can also contral magnetic controlling the current through the Helmholtz cuils, and using calculate the field The only left to determine is the radius of the electron's path through the field The circuit required for this 2 dõé @ - 4 pee = a To find the radius of the beam The equation for circle ardies centered at: point (%o, given by (5) In principle, we could measure the andy coordinates of any three points on the nath of the electron, and solve for andr. However, because the small curvature of the beam in this experiment, this method of calculating ris too sensitive small errors the measurement Recognizing this issne. the manufacturer of the deflection tube has located the luminescent 2 screen within the tube so that the origin of the coordinate system is at the point where the electron beam enters the magnetic field with horizontal velocity. This gives: 1=0 (6) and yo= (7) So. we only need to measure and for single point In the experiment you will adjust the magnetic field. so the electron beam goes through .= 10 cm. y=2cm. Combine equations 5. and 7. and solve for in terms of and for single point on the electrons path. Calculate given 10em and 2em. Thus by measuring V. and (to calculate B). and measuring andy (to calculate r), the mass of the electrons can easily be computed from ed. 4. Data and Data analysis: For different values of acceleration voltage, the current was adjusted each time, so the electron beam ends up at 10cm, y=2cm. Current in the Helmholtz coils then reversed to make the beam deflect in the opposite direction Current adjusted so the electron beam ends up 10cm. y=2cm. The purpose of measuring the currents for positive and negative deflections to minimize any error associated with an initial offset of the beam from horizontal The data collected is given in the table below: V,(V) luo (A) Down (A) lave (A) B[T) B² (T²) 1000 0.0951 0.0844 1500 0.1180 0.1060 2000 0.1366 0.1252 2500 0.1515 0.1407 3000 0.1663 0.1545 Complete the table above, use equation 2 to calculate the magnetic field B. Graph equation so you get the mass of the electrons from the slope of best fit line through your data rather than individual calculations of the mass Use the slope to find the mass of electron Calculate the % error in the mas of election Use regression table find the Am Express your result in the form m Am:

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