Atomic Physics

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Atomic Physics

• Dr. CY Li
• School of physics,
• Nankai University,
• Email licy_at_phys.nankai.edu.cn

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Ch1 Atomic structure

• What is an atom?
• What is inside an atom?
• How big is an atom?
• Charges within the atom
• Thomsons model
• Rutherford scattering

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Some Words

• Charge
• Discharge
• Millikans oil-drop experiment
• plum-pudding
• Scattering
• planetary model
• Atomizer

• Atom
• Electron
• Nucleus
• hydrogen
• Carbon
• Apparatus
• Cathode
• Anode

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What is an atom?

• An atom is the smallest unchangeable component of
  a chemical element. It is the basic element
  making up a molecule.
• It is very small with a radius about 10-10 m.
• It consists of a nucleus and electrons moving
  around the nucleus.
• It is electrically neutral, with a nucleus of
  positive charge and electrons.
• Its mass varies.

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Relative atomic masses

• A relative mass called atomic mass unit (u) is
  used to mark the mass of atoms.
• The unit of atomic mass is based on the carbon
  atom, that is, the mass of carbon-12 is equal to
  12.00000u.
• Or 1u1/12 of the mass of a neutral carbon atom
  with nuclear charge 6 and mass number 12.
• 1u is approximately equal to the mass of a
  hydrogen atom. M(H)1.0079u

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The absolute atomic masses

• Using Avogadros constant NA,
• For example, oxygen, the atomic mass is 15.999
  and its absolute mass is 26.558x10-27 kg.

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The size of atoms

• The mass number of atoms is defined as the mass
  of one mole in the unit of gram.

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How were electrons found?

• Gaseous discharge The discharge of electricity
  through a gas can be caused by an electric field
  at a certain pressure.
• The discharge is a violent spark as the gas
  suddenly changes from being an excellent
  insulator to being a good conductor.
• Cathode rays could be deflected by both electric
  and magnetic fields and they are negatively
  charged.

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Electron charge-to-mass ratio measurement

• Thomson undertook a quantitative study of cathode
  rays in 1897. It was shown that their
  charge-to-mass ratio is a constant.
• Using the apparatus shown in Fig1.1 in P7, the
  speed could be measured when cathode rays have no
  deflection, that is, the electric force equals
  the magnetic force.
• The ratio was measured when only the magnetic
  field was applied and the rays were in a circular
  motion.

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Charge of electrons

• Millikans oil-drop experiment was done in 1911
  to measure the charge of the electron. The charge
  of small drops of oil is determined from their
  motion in the electric field.
• There are two different forces acting on the
  oil-drop
• Electrostatic force, qV/d,
• Gravitational force, mg,
• The simplified result
• q mgd/V
• q 1.59E-19C

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Millikans oil drop experiment

• When air viscosity is considered, there are four
  different forces acting on the oil-drop
• Electrostatic force
• Gravitational force
• Buoyancy in the air
• Friction with the air
• The value of vg (terminal speed for falling
  droplet) is determined for a particular drop with
  the electric field off, and ve (rising droplet)
  for the same drop is observed with the field on.
• q1.602E-19C

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Thomsona model of atom

• In the early 20th century, the English physicist
  JJ Thomson proposed a model.
• The atom is regarded as a heavy positive sphere
  of charge seasoned with enough electron plums to
  make it electrically neutral. It is called
  plum-pudding atomic model.
• The positive charge was spread throughout the
  atom in which the electrons were imbedded in the
  sphere.

13
Rutherford scattering

• New Zealand physicist Ernest Rutherford has his
  coworkers directed a beam of alpha particles at a
  thin gold foil, they found that some were
  deflected (scattered) at large angles, even
  backward. They found that 1/8000 of particles
  were deflected at an angle larger than 90
  degrees. Demo
• This could not be explained by Thomsons model.
  In this model, you would expect all particles to
  pass nearly straight through the foil with the
  maximum deflecting angle being 0.015 degrees at
  the boundary of the sphere.

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Rutherfords astonishment

• It was quite the most incredible event that has
  ever happened to me in my life. It was almost as
  incredible as if you fired a 15-inch shell at a
  piece of tissue paper and it came back and hit
  you.

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Experimental setting up

• The alpha particles, which are emitted by
  naturally radioactive material radium, pass
  through a collimator (???) and strike a thin
  metal foil. Passed particles will make the zinc
  sulfide screen flash when striking it.
• The entire apparatus is placed in a vacuum
  chamber.

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Rutherfords nuclear atom

• When alpha (a) particles passing through a thin
  gold foil, the most of a particles were scattered
  with small angles, but a significant fraction
  were scattered through much larger angles.
• This led to the nuclear atom a tiny nucleus
  containing all the positive charge of the atom
  and most of its mass, surrounded by electrons.

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Coulomb Scattering

• The particles will be scattered due to the
  Coulomb force.
• Scattering angle The angle between the
  directions of the deflected and the incident
  particle beams.
• The impact parameter b the distance of closest
  approach of the alpha particle to the target
  nucleus when no deflection occurs.

• Coulomb scattering

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Rutherford scattering formula

• Rutherford scattering formula

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How to determine the scattering angle?

• As indicated by the scattering formula, the angle
  of scattering depends on three factors
• The initial speed of the alpha-particle,
• The charge on the core,
• The aiming of the alpha-particle,

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Further experiments

• Geiger and Marsden varied the thickness and the
  metal of the foil. Four predictions of the
  scattering formula were tested
• N(?) vs t, scattering rate vs foil thickness,
• N(?) vs Z2, scattering rate vs the nuclear charge
  Z,
• N(?) vs 1/K2, scattering rate vs the kinetic
  energy of alpha particles,
• N(?) vs 1/sin4(? /2), scattering rate vs the
  scattering angle

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How to explain alpha-particle scattering

• It can be explained by coulomb forces between the
  particle and the nucleus.
• An alpha-particle passing near the nucleus is
  subject to an increasingly large coulomb
  repulsion as the distance between them decreases.
  
• As the atom in mostly empty, many of the
  alpha-particles go through the foil without
  deviation. But an alpha-particle coming close to
  a nucleus experiences a very large force exerted
  by the massive, positive core, and is deflected
  through a large angle.

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The planetary model

• The electrons move around the nucleus in some
  fashion like the planets revolving around the
  sun.
• The difficulties
• Radiated electromagnetic waves produced by moving
  electrons would carry away energy. The electrons
  would move more and more close to the nucleus and
  eventually collapse into it.
• You would also expect electromagnetic radiation
  of all wavelengths emitted instead of certain
  quantised frequencies in reality.