Physics I Class 24 e/m Ratio for the Electron Rev. 14-Apr-04 GB 24-1 Joseph John (“J.J.”) Thomson J.J. Thomson 1856-1940 J.J. Thomson was appointed in 1884 as the third Cavendish Professor (head of the Cavendish Laboratory) at Cambridge, after James Clerk Maxwell and Lord Rayleigh. In 1899, his experiments with cathode ray tubes led him to postulate the existence of a new particle with a ratio of charge to mass (e/m) far larger than the same ratio for a positive hydrogen ion. The word “electron” was coined in 1891 by G. Johnstone Stoney. Today we will measure e/m for the electron. 24-2 Calculating Change in K.E. from Electric Potential (Review) final e K U 0 or K U U q V (e) V or U (e) V K ( e)( V ) (1.6 10 19 ) (100) 1.6 10 17 J If the electron starts at rest (or very close to it), then V = 100 initial V = 50 e 1 2 m v 2 e V V=0 24-3 Magnetic Force on a Moving Charge (Review) F q vB charge of the particle (C; + or –) v : velocity of the particle (m/s) B : magnetic field (T) q: Force is at a right angle to velocity. Force is at a right angle to magnetic field. Important: If q is negative, that reverses the direction of force. 24-4 The Radius of the Circle (Review) F r v Although the directions of the vectors are changing, the magnitudes stay the same. v2 F ma m r F qvB v2 qvB m r v2 mv rm qvB qB 24-5 Apparatus for Measuring e/m We will set Potential in tube (V). Current in coils (I). We will observe Radius of circular electron path (r). We will calculate e/m. 24-6 The Cathode Ray Tube Electrons Electrons are randomly kicked out of the metallic cathode by thermal energy. Once free of the metal, the electrons are accelerated through a potential difference of V from cathode to anode. 24-7 Analysis of Electron Acceleration cathode anode K U U (e) V K (e)[ V ] Electron Stream pot = -V pot = 0 e [0 ( V )] e V Electrons have very low kinetic energy when they leave the cathode – essentially zero. m v2 e V 2eV v m 1 2 or 24-8 Helmholtz Coils Magnetic Field Helmholtz Coils are designed to have a nearly uniform (constant) magnetic field in the center. The field direction is along the axis of the coils. The magnitude is proportional to I, the current. The formula to calculate this is a Physics II topic, but for our coils, B 7.8 10 4 I where B is in tesla and I is in amperes. 24-9 Derivation of e/m Formula r mv eB e v m rB v 2eV m 2eV e 2V e e 2V m m m rB rB m rB 2V e m rB or 2V e 2 2 m r B We set or observe all of the variables on the right side of the equation. 24-10 Experimental Procedure 1. Turn up V to get an electron beam. Record V. 2. Turn up I (to make B) until the electrons make a complete circle. Record I. 3. Observe r – use the mirrored scale in the rear. 3a. Or (easier): Adjust I until the electrons just hit the far side of the tube. This is a known radius (5.57 cm). Record I. 4. Repeat three times with different values of V. 24-11 Viewing the Electron Path 24-12 A Similar Application -Mass Spectrometer Definition from chemistry: “Mass spectrometers use the difference in mass-to-charge ratio (m/e) of ionized atoms or molecules to separate them from each other. Mass spectrometry is therefore useful for quantitation of atoms or molecules and also for determining chemical and structural information about molecules. Molecules have distinctive fragmentation patterns that provide structural information to identify structural components.” 24-13 Basic Operation of a Magnetic Sector Mass Spectrometer Stage 1: Ionization The atom is ionized by knocking one or more electrons off to give a positive ion. This is true even for things which you would normally expect to form negative ions (chlorine, for example) or never form ions at all (argon, for example). Mass spectrometers always work with positive ions. Stage 2: Acceleration The ions are accelerated so that they all have the same kinetic energy. Stage 3: Deflection The ions are then deflected by a magnetic field according to their masses. The lighter they are, the more they are deflected. The amount of deflection also depends on the number of positive charges on the ion – in other words, on how many electrons were knocked off in the first stage. The more the ion is charged, the more it gets deflected. Stage 4: Detection The beam of ions passing through the machine is detected electrically. 24-14 Mass Spectrometer Diagram Adjusting the accelerating potential (V) and/or the magnetic field (B) “tunes” the spectrometer to detect only ions with a specific ratio of charge to mass. 24-15 Class #24 Take-Away Concepts 1. 2. The ratio of e/m is determined by accelerating a stream of electrons through an electric potential difference and observing their path in a magnetic field. The formula for e/m (know how to derive it): 2V e 2 2 m r B 3. Mass spectrometers work by the same principle. 24-16 Activity #24 Measuring e/m for the Electron Objective of the Activity: 1. 2. Work through the analysis steps to get the e/m formula. Take your own measurements and compare your value of e/m for an electron with the known value. (1.76 x 10+11 C/kg) 24-17 Optional Material for Class #24 How do we know the mass of an electron? This is a great question! We just measured e/m for an electron using table-top instruments that would have been available (in some form) 100 years ago. The first accurate measurement of the mass of the electron was made (indirectly) by Robert Andrews Millikan in 1910. How did he do it? 24-18 Robert Andrews Millikan R.A. Millikan 1868-1953 Oil Drop Experiment (1910) At the University of Chicago in 1910, Millikan developed his famous oil drop experiment to determine the charge on an electron. An atomizer sprayed small oil droplets into the top chamber. Some of them fell through a small hole into a second chamber. X-rays caused the air in the second chamber to become ionized. The drops in the second chamber picked up a small (variable) number of electrons. They were acted upon by both the force of gravity and an opposing electrical force created by an adjustable electrical potential difference between the top and bottom. 24-19 Analysis of Oil Drop Experiment QE 1. 2. Q Oil Drop 3. Mg With E = 0, the terminal velocity of the drop falling through air allows calculation of its mass (M) via a known mathematical relationship. Once M is known, E is adjusted so that the drop is in equilibrium (drop stopped). Then Q is determined: 4. Mg E Steps 1 and 2 are repeated many times. Each drop has a different M and Q, but when enough drops are examined, the smallest difference between different Q values is found to be e, the charge on one electron (ignoring the – sign). The mass of the electron is 1 e m e (1.76 10 11 ) 1 (1.6 10 19 ) 9.1 10 31 kg m 24-20