Electrons

1
Electrons

• Thermionic Emission
• Deflection of Electrons in Electric Field
• Deflection of Electrons in Magnetic Field
• Determination of e/m
• Cathode Ray Oscilloscope

2
Thermionic Emission (1)

• When a metal is heated sufficiently, its free
  electrons gain enough kinetic energy to leave the
  metal. This process is called thermionic
  emission.

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Thermionic Emission (2)

• In practice, thermionic emission is caused by
  heating a filament of metal wire with an electric
  current.

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Thermionic Emission (3)

• The work done on each electron from the filament
  is
• W eV
• where V is the p.d. across the filament and the
  anode.
• Electron-volt
• The electron-volt is an amount of energy equal
  to the work done on an electron moved through a
  p.d. of 1V.

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Properties of Electron Beams (Cathode rays)

• Cathode rays travel in straight lines.
• Cathode rays can cause fluorescence.
• Cathode rays can be deflected by electric field
  and magnetic field.
• Cathode rays may produce heat and X-rays.
• Cathode rays can affect photographic plates.

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Deflection of Electrons in a Uniform Electric
Field (1)

• Consider an electron beam directed between two
  oppositely charged parallel plates as shown
  below.
• With a constant potential difference between the
  two deflecting plates, the trace is curved
  towards the positive plate.

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Deflection of Electrons in a Uniform Electric
Field (2)

• The force acting on each electron in the field is
  given by

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Deflection of Electrons in a Uniform Electric
Field (3)

• The vertical displacement y is given by

This is the equation for a parabola.
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Deflection of Electrons in a Uniform Magnetic
Field (1)

• The force F acting on an electron in a uniform
  magnetic field is given by

Since the magnetic force F is at right angles to
the velocity direction, the electron moves
round a circular path.
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Deflection of Electrons in a Uniform Magnetic
Field (2)

• The centripetal acceleration of the electrons is

Hence
which gives
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Determination of Specific Charge - e/m
J. J. Thomson
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Determination of Specific Charge Using a Fine
Beam Tube (1)

• The principle of the experiment is illustrated by
  the diagram below.

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Determination of Specific Charge Using a Fine
Beam Tube (2)
and the kinetic energy of the electron
provided by the electron gun is
Where V is the anode voltage.
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Determination of Specific Charge Using a Fine
Beam Tube (3)
Rearrange the equation gives
The value of the specific charge of an
electron is now known accurately to be
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Thomsons e/m Experiment (1)
Thomsons apparatus for measuring the ratio e/m
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Thomsons e/m Experiment (2)

• A beam of electron is produced by an electron gun
  with an accelerating voltage V.
• The electron beam is arranged to travel through
  an electric field and a magnetic field which are
  perpendicular to each other.
• The apparatus is set-up so that an electron from
  the gun is undeflected.

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Thomsons e/m experiment (3)

• As the electron from the gun is undeflected, this
  gives

Combining the equations, we get
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Cathode Ray Oscilloscope (CRO)

• The structure of the cathode ray tube

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Uses of CRO

• An oscilloscope can be used as
• 1. an a.c. and d.c. voltmeter,
• 2. for time and frequency measurement,
• 3. as a display device.

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Lissajous Figures (1)

• Lissajous figure can be displayed by applying
  two a.c. signals simultaneously to the X-plates
  and Y-plates of an oscilloscope.
• As the frequency, amplitude and phase difference
  are altered, different patterns are seen on the
  screen of the CRO.

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Lissajous Figures (2)
Same amplitude but different frequencies
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Lissajous Figures (3)

• Same frequency but different phase

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