Four Chapter 6

Some Interesting Applications

• Many applications of the principles discussed so far involve the directing of electrons or protons, which are in a beam, to specific locations.
• The directing can be done by
  • electric fields only
  • magnetic fields only
  • both electric and magnetic fields
• Consider the following example.
  • Electrons are accelerated through a potential difference of 36.9 V. The electrons pass through a narrow slit to form a beam. The beam of electrons pass into a region where there is a magnetic and electric field present. The electric field is produced by two parallel plates 0.15 m apart with a potential difference of 12 V between them. What strength of field must be present to cause the undeflected passage of the electrons? Note that the mass of the electron is 9.11 X 10^-31 kg.

Cathode Ray Tube

• Oscilloscope - A device used to analyse and measure electrical signals
  • Historically, oscilloscopes used a cathode ray tube
• In the past, television sets also used cathode ray tubes to produce the pictures on the screen.

Components

• The cathode ray tube consists of:
  • An electron gun
  • Horizontal and vertical deflecting plates or coils
  • A fluorescent screen

Operation

• The heater wire heats the cathode. Electrons are emitted by thermionic emission.
• Thermionic emission - the process whereby electrons are emitted by a hot filament.
• These electrons are accelerated towards an anode with a small central hole.
• The velocity of the electrons is determined by the process described in the example given above. The electrons gain energy by acceleration through a potential difference.

• Electrons passing through the hole, enter a region where we find:
  • vertical and horizontal deflecting plates, which set up electric fields in order to transmit forces to the electrons. These forces direct the electrons in the desired way. The equation of force is F = qE (E is electric field not energy in this formula)
  • vertical and horizontal deflecting coils, which set up magnetic fields in order to transmit forces to the electrons. The equation of force is F = qv X B. As with the deflecting plates, electrons are directed to desired locations.
  • a combination of vertical and horizontal coils and/or deflecting plates, which again transmit forces to the electrons by creating electric and magnetic fields.
• Once the electrons are headed in the desired direction, they fall onto a fluorescent screen, which absorbs the kinetic energy of the electrons. The fluorescent screen then radiates this energy as visible light.
• A control grid may be placed between the cathode and the anode. This grid is used to increase or decrease the kinetic energy of the electrons, so that the brightness of the light given off by the fluorescent screen can be controlled.
• As pointed out above, oscilloscopes historically have used cathode ray tubes.
  • Oscilloscopes permit amplification and observations of electrical signals. These were displayed in a stationary pattern on the screen of a cathode ray tube.
  • Within the electronics of the oscilloscope is a horizontal sweep circuit
    • Deflects the beam horizontally (left to right).
    • then returns to the start point usually with the beam turned off
    • sweep cycle is then repeated
    • Sweep period can be varied from a few seconds to a few microseconds
    • A triggering circuit can synchronize the start of each sweep with the same point in the repetitive wave form being examined.
    • The signal being analysed is then applied to the vertical deflection plates (or coils) so that in addition to horizontal sweeps, there is vertical deflection.
    • The beam makes a visual plot of the variation of the potential difference in the signal with time.
    • The vertical scale (potential difference) and the horizontal scale (time) can be adjusted to make the trace stationary and a convenient size.

Mass Spectrograph

Mass Spectrometer - (Spectrograph) A device used to measure the mass of charged particles.

• Heating or an electrical discharge at S produces the ions.
• The ions drift through S₁ and are accelerated through a potential difference to S₂.
• The velocity of the particle at S₂ can be calculated by using:

qV = 1/2(mv²) Equation I

• Ions travelling with velocity v enter the magnetic field B which provides a centripetal force. This force can be calculated by using:

qvxB = (mv²)/r Equation II

• Rearranging equation I for velocity, substituting into equation II, and rearranging for mass gives:

m = (qB²r²)/2V Equation III

• The ions strike and expose a photographic film at point a.
• The radius of the circular path can be measured, and if the charge q, magnetic field strength B, and the accelerating potential V are known, equation III can be used to calculate the mass of the ion.
• Note that the larger the radius of the path, the more massive the ion. The particle that lands at b will be more massive than the one which lands at a.
• Many mass spectrometers use velocity selectors (electric and magnetic fields used simultaneously to permit only particles of a given velocity to travel on a straight path (See example before cathode ray tube above for a velocity selector).
• The mass spectrograph led to the discovery of isotopes.
  • Isotopes - atoms of an element with different masses.
    • have the same number of protons
    • have the same number of electrons for a neutral atom
    • have different numbers of neutrons.

January 17, 2014