Physics · Ch 8 — Atomic and Nuclear Physics
Determination of specific charge e/m of an electron - Thomson's experiment
Determination of specific charge e/m of an electron - Thomson's experiment
J.J. Thomson's 1887 experiment measured the "specific charge" of the electron - its charge-to-mass ratio - and is regarded as one of the landmark experiments marking the birth of modern physics.
Apparatus. A highly evacuated discharge tube produces a narrow beam of cathode rays (electrons) that passes through a pinhole in the anode disc A, then between a pair of parallel deflecting plates held at high voltage, and the whole assembly sits between the pole pieces of a magnet so that the electric field and magnetic field act perpendicular to each other and to the beam. Where the beam finally lands on a zinc-sulphide-coated fluorescent screen is observed as a bright scintillation spot.
Step 1 - velocity selection. With both fields on, their strengths are adjusted so the beam lands exactly at the original undeflected point O. This means the electric force and magnetic force on the electron exactly balance: , so the beam's velocity is
Step 2 - specific charge from energy. Since the beam accelerates from cathode to anode through potential difference , its potential energy converts entirely to kinetic energy: , so
Substituting measured values of , and gives .
Step 3 - specific charge from pure electric deflection. With the magnetic field switched off, the electron (initial vertical velocity zero) undergoes projectile-like deflection over the plate length : its deflection at the plate edge is , and since the deflection measured on the distant screen is proportional to by a geometric constant (i.e. ), this can be rearranged to
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What this figure shows. This figure shows the full experimental layout: a highly evacuated discharge tube in which cathode rays produced at the cathode are accelerated toward an anode disc A that has a pinhole to select a narrow beam. That beam then passes between a pair of parallel deflecting plates maintained at a high voltage, and the whole tube sits between the pole pieces of a magnet so that the electric field and the magnetic field act on the beam simultaneously and perpendicular to each other. The beam finally lands on a fluorescent screen coated with zinc sulphide, where it produces a visible glowing spot whose position O (undeflected) or P/P' (deflected) is what Thomson measured to extr …
What this figure shows. This figure illustrates the velocity-selector configuration used in the first stage of Thomson's method: the electric field E and magnetic field B are arranged so that the electric force F_E on the electron and the magnetic force F_B on the electron point in opposite directions and are adjusted to exactly cancel. When this balance eE = ev B is achieved, the electron beam travels in a straight line through the crossed fields and lands back at the original undeflected spot O on the screen, and the velocity of the beam is then simply read off as v = E/B, which is the first quantity Thomson needed before he could i …
What this figure shows. This figure shows the beam's parabolic-style deflection when only the electric field between the plates acts on it (the magnetic field switched off): the electron enters horizontally, is pushed vertically by the field over the length l of the plates, and exits with a small vertical displacement y' at the edge of the plates, which translates into a larger deflection y measured on the distant screen. The diagram labels the plate separation region, the direction of the field, and the geometry (length l, screen deflection y, y') that Thomson used in the kinematics of projectile-like motion to derive the deflection formula in terms of e/m, the plate …