CIE A Level Physics (9702) 2019-2021

Revision Notes

25.3.6 Charge to Mass Ratio of Electrons

Charge To Mass Ratio of Electrons

  • The velocity of an electron beam can be found using a deflection tube
  • This consists of electrons accelerated from a cathode (negative terminal) to an anode (positive terminal)
  • They are then passed between two oppositely charged parallel horizontal plates and a magnetic field is applied perpendicular to them
  • This means an electron beam is passed through a combined electric (E) and magnetic (B) field
  • By adjusting the strengths of the E and B fields, the two electric and magnetic forces can be made to balance the path of the electrons and keep the beam horizontal
  • When the electron beam remains straight, the electric and magnetic forces on them are equal in magnitude but opposite in direction
  • The magnetic field is provided by two coils (Helmhol coils) which provide a uniform field between them
  • The force due to an electric field is given by:

F = eE

  • The force due to a magnetic field is given by:

F = Bev

  • Equating the E and B forces gives:

eE = Bev

  • Where:
    • e = charge of an electron (C)
    • E = electric field strength (N C-1)
    • B = magnetic flux density (T)
    • v = velocity of the electron beam (m s-1)
  • Rearranging for the velocity v, and using the definition of electric field strength between two plates, the equation becomes:

Charge To Mass Ratio of Electrons equation 1

  • Where:
    • V = voltage between the plates (V)
    • d = distance between the plates (m)

Measuring the charge-to-mass ratio of the electrons

  • When electrons travel through a magnetic field that is perpendicular to its velocity, they travel in a circular path
  • This means the magnetic force, which is perpendicular to its velocity, is equivalent to the centripetal force:

Charge To Mass Ratio of Electrons equation 2

  • Where:
    • r = radius of the circular path of the electrons (m)
    • m = mass of an electron (kg)
  • Rearranging this for the charge to mass ratio e/m gives the equation:

Charge To Mass Ratio of Electrons equation 3

  • This is equivalent to 1.76 × 1011 C kg-1
  • A common analytical tool used to measure the charge-to-mass ratio of particles is a mass spectrometer

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