24.3 Charge to Mass Ratio of Electrons

In Thomson's experiment, the arrangement with a crossed (perpendicular) pair of uniform electric and magnetic fields is called a velocity selector.  If charged particles with various velocities enter the fields, only those whose velocity is perpendicular to both fields and whose speed satisfies $v_{\perp }=\frac{\left|\stackrel{\rightharpoonup }{E}\right|}{\left|\stackrel{\rightharpoonup }{B}\right|}$  will continue in a straight line.  This arrangement is, therefore, able to select charged particles of a given velocity from all other particles by setting the fields to appropriate values.  Velocity selectors have an application in mass spectrometers.

The arrangement can be used to measure the speed of charged particles.  One must adjust the electric and magnetic fields until there is no deflection and then use the equation to solve for the speed.  Note that the value of the speed for which there is no deflection depends on neither the charge nor the mass of the particle.  Therefore, you can use a velocity selector to measure the speed of charged particles even if you do not know their charge or their mass like in the simulation.

Given the definitions of the inward, centripetal force and the magnetic force, it is possible to derive an equation for the charge-to-mass ratio of the particle exhibiting circular motion in the magnetic field alone.

In a Thomson-style experiment, the velocity is first determined using both a known magnetic and electric field.  Then, by turning off the electric field and measuring the radius of the circular path made by the charged particles, you would be able to determine the charge-to-mass ratio of the particles.

Turn off the electric field strength by setting it to 0 V/m in the charge-mass simulation, but leave the magnetic field strength at 2.00T and the speed at 50.0 m/s.  Allow the simulation to run by pressing play.  The data will now display the radius, r. Record this value below and use it in the formula above to determine the charge to mass ratio used in the simulation.

r = ____ m

Thomson determined that the charge-to-mass ratio of the particles in a cathode ray was 1.76 × 1011 C/kg.  This value was unique to all cathode rays regardless of the metal electrodes used to produce them.  Thomson had discovered the electron, but, more importantly, he had determined that the charge-to-mass ratio for an electron was thousands of times larger than that of a hydrogen ion, which meant that the electron was a "subatomic" particle.  He proposed a radical idea at the time - the atom was divisible into smaller particles.  And, because no positive subatomic particles had been discovered at the time, he suggested that the atom consisted of electrons embedded in a blob of massless positive charge, what is now known as the raisin-bun model of the atom. You will learn more about this model later on in the lesson.