Ideas of Modern Physics

1
Ideas of Modern Physics

• And when Water and Oil of Vitriol poured
  successively into the same Vessel grow very hot
  in the mixing, does not this heat argue a great
  Motion in the Parts of the Liquors? And does not
  this Motion argue, that the Parts of the two
  Liquors in mixing coalesce with Violence, and by
  consequence rush towards one another with an
  accelerated Motion?
• -Isaac Newton

2
Premonitions

• Newton could not help being impressed with his
  own mechanics and theory of gravitation.
• He was also aware of how little he knew about
  matter and about light.
• The intuitive description of chemical reactions
  in his own mechanical terms perhaps contained a
  germ of atomic theory.
• Only many increasingly incisive experiments and
  theories concerning diverse physical phenomena
  would lead to conclusive answers.

3
Review

• Einsteins analysis of Brownian motion determined
  the mass of the hydrogen atom m_H(gm)1/N_A where
  Avogadros number is 6.02e23
• Through electrolysis, Faraday related hydrogen
  mass to charge 8600 CN_A e determining e
• Millikans oil drop experiment measured e 1.602
  e-19 C directly.
• Thomson measured the ratio e/m_e for cathode ray
  electrons and given e found m_e was tiny compared
  to m_H.
• Discovery of nuclear radioactivity would provide
  probes of atomic structure.

4
Radiation

• Unstable atoms spontaneously emit radiation of
  various kinds, both electrically neutral and
  electrically charged.

5
Exponential decay law

• Decay processes are uncontrolled but follow a
  simple statistical law.
• The probability an unstable nucleus has decayed
  after time t is Pexp-t/tau where tau is the
  lifetime.
• Given N objects, the average change dN in a small
  time interval dt is the rate of decay dN/dt
  -N(t)/tau

6
Kinds of rays

• Alpha particles are less penetrating still and
  positively charged. They turn out to be He
  nuclei.
• Beta rays are less penetrating negatively charged
  particles. They turn out to be energetic
  electrons.
• X, gamma rays are penetrating and electrically
  neutral. They turn out to be quanta of
  electromagnetic radiation. X-rays may be radiated
  by electrons. More energetic gamma rays are
  radiated by energetic protons in a nucleus.

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Alpha particle emission

• Some radioactive nuclei spontaneously fission
  (fall apart) into smaller nuclei releasing
  neutrons and fragments like (pnpn), a He-4
  nucleus.

Sg-263(106p,157n)gtRf-259(104p,155n)He-4(2p,2n)
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Alphas are He nuclei

• In 1909, Rutherford established that so called
  alpha-particles are in fact He-4 nuclei by
  collecting He gas created by neutralized alphas.

http//webserver.lemoyne.edu/faculty/giunta/EA/ROY
DSann.HTML
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Beta particle creation

• A free neutron weighs a bit more than a proton
  and decays to a proton plus an electron plus a
  (neutral neutrino)- ngtp,e,nu - in about 13
  minutes.
• Within a nucleus, this process is suppressed
  because the neutron is tightly bound and
  conversion to a proton requires more energy than
  is available.

10
Radioactive beta decay

• An excess neutron in a nucleus close to the edge
  of stability can decay. The rate is suppressed
  and may require millions or billions of years but
  in a gram containing N_A1e24 nucleons be
  observable.
• A neutron is transformed into a proton and the
  electron and neutrino fly out - the elemental
  nucleus is transmuted.

C14 (6p,8n)gt N14(7p,7n) e nu
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Subnuclear beta decay

• A proton differs from a neutron by the flavor of
  on quark puud, nudd.
• Neutron results from the weak interaction of
  quarks in which a down quark radiates a W boson
  which decays to electron and neutrino dgtu W-,
  W- gt e- nu
• The neutrino was not observed directly until the
  1950s when nuclear reactors were available which
  produced vast numbers of unstable nuclei and
  neutrinos.

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Example

• Lead Pb has Z82 and stable isotopes with A 206
  (26),207(21),208(52)
• The isotope with A210 is unstable.
• Pb-210 gt Bi-(210) e- nu, tau 20 years.

13
Gamma and X-rays

• Like atoms, nuclei have excited internal states
  and strong or weak decay may result in an excited
  nucleus which then decays emitting
  electromagnetic radiation
• Example. In beta decay, the proton may recoil
  against the e and nu so is rattling around inside
  the nucleusCo-60 gt Ni-60 e nu, Ni60gt
  Ni-60 photon with E(photon) 1.2 MeV (gamma
  energy)

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Geiger counter

• A tube of gas with a charged axial wire.
• Electrons are liberated in the gas and ions
  created by collisions of fast charged particles
  with neutral atoms of by absorption of x-rays
• Electrons drift towards the wire and the ions to
  the wall constituting a small current pulse.

15
Energy in beta decay

• M_n939.56 MeV/c2
• M_p 938.27 MeV/c2 M_n1.29 MeV/c2
• M_e 0.51 MeV/c2 is created
• M_nu0 (at least lt 1 eV/c2!)
• About 0.5 MeV is released as kinetic energy
  shared between the e and nu which are
  relativistic and the proton.

16
Energy in alpha decay

• The binding energy per nucleon is 1 MeV
• The energy release in alpha emission fission is a
  few MeV.
• M_alpha 2M_p2M_n4000 MeV
• The alpha is not relativistic yet carries energy
  equivalent to acceleration through a million volt
  electrostatic potential difference.

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Rutherfords discovery

• In 1906, Rutherford measured the charge to mass
  ratio of alpha particles detecting them with
  photographic emulsion. When mica was in the path
  he found the image blurred. Since an alpha
  particle weighs 8000 times the electron mass, the
  deflections could not be ascribed to scattering
  from electrons.
• In 1909, he suggested Hans Geiger get his
  undergraduate Earnest Marsden to see if an alpha
  could be scattered at a large angle.

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Scattering apparatus

• R radon alpha source
• F target metal foil
• S zinc sulphide screen scintillates when struck
  by an alpha
• M microscope

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Marsden observed large angles

• Rutherford wrote
• Then I remember two or three days later Geiger
  coming to me in great excitement and saying "We
  have been able to get some of the alpha-particles
  coming backward " It was quite the most
  incredible event that 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.

20
Angular distribution

• Rutherford supposed the mass and positive charge
  was compressed into a volume much smaller than
  the atom and calculated the probability of
  scattering through an angle theta.
• The formula fit the data!

21
Splitting the atom

• The fun was just beginning!
• In 1919, Rutherford established that an alpha
  impinging on a nitrogen nucleus can cause a
  hydrogen atom to appear! Newspaper headlines
  blared that Rutherford had "split the atom".
• This was the beginning of nuclear physics when
  yet the real quantum structure of the atom had
  not been established.

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The structure of the nucleus

• The mass numbers A are not equal to the atomic
  charge numbers Z. Why?
• Perhaps for example the alpha particle, the He
  nucleus, with A4 and Z2, was 4 protons and two
  electrons?
• Rutherford suggested perhaps a proton and an
  electron could form not just a hydrogen atom but
  a tightly bound neutral state - a neutron.

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Discovery of the neutron

• A neutron is electrically neutral so does not
  respond to electric or magnetic fields nor
  produce ionization directly.
• Rutherfords student James Chadwick searched for
  and discovered the neutron in 1932 and received
  the Nobel prize in 1935.

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Processes behind discovery

• Hit a nucleus (Be-9) with an alpha particle
  emitted in the decay of Po. It is absorbed to
  form an unstable isotope which releases an excess
  neutron of high energy (6 MeV).
• A neutron encountering hydrogen will eject
  protons which create detectable ionization.

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Measuring recoil proton energies

• Protons knock electrons from atoms thereby losing
  energy and eventually stop.
• The amount of material required to stop them
  determines their energy.

http//dbhs.wvusd.k12.ca.us/Chem-History/Chadwick-
1932/Chadwick-neutron.html
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The size of the nucleus

• The protons and neutrons in a nucleus turn out to
  be close packed into a sphere. The electric field
  is not infinite but in fact goes to zero at the
  center. In scattering electrons from nuclei,
  those which penetrate the nucleus deviate from
  Rutherfords scattering model so are sensitive to
  the nuclear radius.
• Cross check Neutrons interact only via short
  range (contact) nuclear forces so the probability
  of interaction in a sample is proportional to the
  number of nuclei and the cross sectional area of
  a nucleus.

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Summary

• The early part of the 20th century was a tumult
  of new discoveries relating to atomic matter.
• The basic structure of the atom was established
  but much remained to be understood.