Electromagnetism and Quantum Physics

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Electromagnetism and Quantum Physics

• Notes and Equations

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Charge-to-Mass Ratio

• q/m v/Br
• q charge in Coulombs (C)
• m mass in kg
• v velocity in m/s
• B magnetic field strength in Tesla (T)
• r radius of the circular path of an electron

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Thomsons Cathode-Ray Tube

• Thomson used the CRT to measure the
  charge-to-mass ratio of an electron.
• The CRT is a type of vacuum tube that accelerates
  electrons without the electrons colliding with
  air molecules.
• The CRT contains a cathode which is connected to
  the negative terminal of a voltage source.

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Thomsons Cathode-Ray Tube

• The cathode provides a source of electrons.
• The anode is connected to the positive terminal
  of a voltage source which attracts and
  accelerates the electrons.
• At the center of a CRT, electric and magnetic
  fields produce forces that act on the electrons.

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Thomsons Cathode-Ray Tube

• The forces are equal in magnitude, but opposite
  in direction and allowed Thomson to calculate the
  velocity of the electrons.
• Video Clip
• Remember Newtons Second Law?
• a Fnet / m
• Fnet ma
• Fmag Bqv

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Thomsons Cathode-Ray Tube

• Now, remember centripetal force?
• Fcentripetal mac where ac centripetal
  acceleration
• ac v2 / r
• So, Fcentripetal Fnet Fmagnetic Bqv
• Fnet ma Fcentripetal mac mv2 / r
• Now, Bqv mv2/r Solving for q/m v/Br

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Thomsons Cathode-Ray Tube

• Calculation of the mass of an electron.
• First, Thomson calculated the straight-line
  velocity of the of electrons in the CRT.
• Next, he measured the distance between the
  undeflected spot and the position of the spot
  when only the magnetic field acted on the
  electrons.
• Using this, he calculated the radius (r).

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Thomsons Cathode-Ray Tube

• Thomson calculated a value of
• 1.759 x 1011 C/kg for the charge-to-mass ratio
  for an electron.
• Using q 1.602 x 10-19 C, the mass of an
  electron can be calculated to be
• 9.107 x 10-31 kg.

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Example Problem

• Path of an Electron in a Magnetic Field
• m 9.11 x 10-31 kg
• v 2.0 x 105 m/s
• B 3.5 x 10-2 T
• q 1.60 x 10-19 C
• r ?
• Bqv mv2 / r
• r mv/Bq r 3.3 x 10-5 m

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Quanutm Theory

• The Photoelectric Effect the emission of
  electrons when electromagnetic radiation falls on
  an object.
• A photocell is similar to a CRT it is a type of
  vacuum tube where electrons can move without
  colliding with air molecules.
• A potential difference is placed across two
  electrodes to attract electrons to the anode.

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Photoelectric Cell

• The photelectric cell is made of quartz to allow
  UV light to pass through.
• When UV light strikes the cathode, electrons are
  released and alow current to flow from the anode
  to the cathode.
• Not all radiation will result in current only
  radiation above a certain amount, called the
  threshold frequency will produce current.

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Photoelectric Cell

• The greater the intensity of radiation, the
  greater the flow of electrons.
• A photocell has a specific voltage where no
  electrons will have enough kinetic energy to
  reach the anode and no current will flow.
• This is called the stopping potential.

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Photoelectric Cell

• If the stopping potential of a photo cell is 3.5
  V, how much KE will the electrons have?
• KE -qV0
• KE - (-1.6 x 10-19 C)(3.5 V) 5.6 x 10-19 J

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Kinetic Theory

• All matter is made up of small particles.
• Particles of matter are in constant, random
  motion.
• Particles of matter constantly collide with each
  other, causing atoms to vibrate when in the solid
  state.
• The energy of vibrating atoms in a solid can have
  only specific frequencies.

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Energy of a vibrating atom

• E nhf
• E is energy in joules (J)
• n is an integer, such as 0, 1, 2, 3, etc.
• h is Plancks constant, 6.63 x 10-34 J/Hz
• f is frequency of vibration in Hertz (Hz)
• Kinetic Energy of an electron
• KE hf hf0 where f0 is the threshold frequency

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Example Problem

• Stopping potential V0 4.0 V
• Charge of an electron q -1.60 x 10-19 C
• KE ?
• KE -qV0
• KE -(-1.60 x 10-19 C)(4.0 V)
• 6.4 x 10-19 V

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Photon Momentum and Energy

• Photon Momentum
• p hf/c h/?
• c the speed of light (3.00 x 108 m/s)
• Photon Energy
• E hc/ ?
• Plancks Constant Lab
• h qV ?/c