PHY 1020 Lecture 20

ATOMIC NUCLEUS

ATOM VS NUCLEUS:
- atom = nucleus + electrons
- Geiger, Marsden, Rutherford (1908 - 1911):
  scattering experiment showed most particles nearly unaffected, some deflected, a few (1/20000) bounced back
  mass of atom concentrated in small nucleus;
- nucleus (diameter ) contains most of atom's mass;
- atom (diameter ) mostly empty space; electrons are very far away from nucleus.
- what goes on in the nucleus has almost nothing to do with atom's chemistry, and vice versa

INSIDE THE NUCLEUS:
- nucleus made of protons and neutrons = ``nucleons''
  proton (p) discovered 1919 by Rutherford, neutron (n) 1932 by James Chadwick;
- particles in nucleus are tightly bound; binding energy within nucleus much bigger than atomic binding energies
- nucleus can be identified by two numbers:
  atomic number Z and mass number A
- atomic number Z = number of protons in nucleus
- mass number A = number of nucleons in nucleus
  A = Z + N, N = neutron number
- element
  = substance in which all nuclei have same nb. of protons
- atoms neutral
  number of electrons in atom = number of protons
- nuclei of same element can have different number of neutrons
  -- ``isotope'' of an element
- isotopes:
  have same number of protons, different number of neutrons;
  notation:
  (or X-A),
  e.g. are isotopes of uranium;
  different isotopes of elements have in general same chemical properties;
- isotopes of hydrogen:
  = protium (hydrogen), nucleus = proton
  = deuterium, nucleus = deuteron
  = tritium, nucleus = triton;
  natural hydrogen: (1/6000) is D, (1/10million) is T;
  H and D are stable, T is unstable;
  ``heavy water'' =
- atomic mass of element = average mass of atoms of element, measured in atomic mass units u;
- unified atomic mass unit: u =
  defined by mass of C-12 = 12 mass units = 12 u;
  (natural C: mass slightly bigger than 12 due to isotopes C-13, C-14)

STRONG FORCE

(also called strong nuclear force, nuclear force)
the e.m. force holding the atoms together is many times ( times bigger than the gravitational force;
in nucleus, many (positively charged) protons packed closely together, repel each other -- nucleus should fly apart; doesn't -- there must be a a force holding it together;
strong force:
- is strongest known fundamental force
  (about 100 times e.m. force);
- attractive
- range of force between nucleons very short: force for distances
  (note that e.m. and gravitational forces have long range)
- charge independence: force same for pp, pn, nn
in ``large'' nucleus (nucleus with many nucleons):
proton at surface attracted only by 6 to 7 nearest neighbor nucleons (due to short range);
e.m. force long-range
e.m. repulsion acts between any two protons in nucleus;
e.m. repulsion grows with number of protons, while strong attractive force on this proton constant;
if Z too large, e.m. repulsion overcomes strong attraction, nuclei with Z > 83 are not stable;
also, expect number of neutrons larger than number of protons for heavy nuclei.

RADIOACTIVITY

nuclide = given species of nucleus
radionuclide (or radioisotope) = nuclide that decays spontaneously
radioactivity, or radioactive decay = spontaneous process of nuclei undergoing a change by emitting particles or rays.
(uranium decay discovered by Henri Becquerel 1896,
radioactive elements radium and polonium discovered by Maria Sklodowska-Curie and Pierre Curie, 1898)
types of radioactive decays:
alpha, beta, gamma decays, (and fission)
decay equation: ;
A = ``parent'', B = ``daughter'', b = emitted particle;
in all decays, charge and nucleon number is conserved;
alpha ( ) decay:
= change of nucleus into a nucleus of another element, with emission of an ``alpha'' particle (= a He nucleus);
alpha decay common for elements with Z > 83;

examples:

effect of alpha decay on nucleus:
alpha particle is a particularly stable nucleus;
alpha decay of heavy elements in Earth's interior keeps Earth hot inside and provides terrestrial supply of He.
beta ( ) decay:
= change of a nucleus into a nucleus of another element, with emission of a ``beta'' particle (= electron) and a neutrino;
example:

effect of beta decay on nucleus:
(i.e. a neutron in the nucleus is converted into a proton)
the beta decay puzzle and the neutrino
early mysteries in beta decay:
- apparent non-conservation of energy:
  energy conservation would require the kinetic energy of the electron to have a well-defined value (given by difference in mass of nucleus before and after decay), but electrons had continuous spectrum, with max. value = value expected from energy conservation;
  ``missing energy''
- apparent non-conservation of angular momentum:
  example:
  
  C-14 was known to have spin 0 and N-14 spin 1, and electron has spin 1/2;
  incompatible with angular momentum conservation;
- neutrino hypothesis (Wolfgang Pauli, 1930):
  there exists a neutral, spin 1/2 particle which is emitted simultaneously with the electron in beta decay.
- this hypothesis resolved both difficulties.
- neutrino observed in 1956 (Clyde Cowan, Frederick Reines)
gamma ( ) decay:
nucleus emits ``gamma'' ray (= energetic photon) and becomes less energetic form of same nucleus (= de-excitation of nucleus from excited state to ground state).
example:

(asterisk means Pb nucleus is excited);
gamma decays always occur when nuclei produced in an excited state, (e.g. as result of alpha or beta decay);
gamma decays analogous to photon emission in atomic de-excitation, but energies of nuclear gamma rays much higher (thousands or million times) than atomic photon energies.
nuclei with atomic number greater than 83 are always radioactive, and undergo series of alpha, beta and gamma decays until stable nucleus is reached.
decay chains:
series of decays beginning with U-238, ending with Pb-206

HALF-LIFE

radioactive decays occur spontaneously; cannot predict when individual nucleus will decay, can only give probability that it will happen;
for a given nuclide, the probability to decay is constant in time; as a consequence, for any time period of a given length, a certain fraction of the available nuclei will decay.
half-life = that time period during which half of the nuclei decay;
i.e. after one half-life, 1/2 of nuclei remain; after two half-lives, 1/2 times 1/2 = 1/4 of the original number remain; etc.
activity of a radioactive sample = number of decays per unit time (unit = 1 Becquerel = 1 decay per second)
half-lives span wide range:

RADIOMETRIC DATING

the rate of decay is constant, independent of temperature, pressure, electrical or magnetic fields, type of molecule in which nucleus is bound,...
rate can serve as ``clock'' for dating ancient rocks and remains of dead plants and animals.

DATING OF ROCKS
- measure ratio of amount of daughter nuclide to amount of parent nuclide
- need to know how much of daughter nuclide is ``primordial'', i.e. in rock from other sources than radioactive decay of parent nuclide -- have to correct for this;
- example: dating of rocks using Pb-208 vs U-238:
  - U-238 (half-life = y) decays via long decay chain, ending up in lead, Pb-206.
  - measure amount of U-238, Pb-206, Pb-204 in the rock;
  - Pb-206 from U decay = ``radiogenic lead'', non-radiogenic lead = ``primordial lead''; Pb-204 is all primordial;
  - deduce amount of radiogenic Pb-206 from known ratio of Pb-204 to Pb-206 and amount of Pb-204,
  - from ratio of Pb-206 to U-238, deduce number of half-lives since rock solidified, with well-defined content of U-238
- check procedure by also meassuring ratio of Pb-207 to U-235 (U-235 decays with half-life of y)
- result of dating of old rocks on Earth:
  oldest rocks on Earth are 3.8 billion years old; meteorites: 4.4 to 4.6 billion years old; oldest Moon rocks returned to Earth by Apollo mission: 4.5 billion years;
- conclusion: Earth is about 4.6 billion years old
CARBON DATING

(Willard F. Libby, 1950):
- , a radioactive isotope of carbon, is formed in Earth's atmosphere due to cosmic radiation;
- bound in , used by plants in photosynthesis, plants ingested by animals
- all living matter has about the same level of radioactivity due to C-14 (15 decays per minute per gram of carbon, corresponding to about carbon atoms being C-14)
- dead animals or plants: C-14 not replenished activity drops (half-life = 5730 years)
- from measurement of activity, can deduce time since C-14 take-in ceased.
- in principle, can use this method to date organic material up to about 50000 years, but possible source of errors in carbon-dating: due to changes in intensity of cosmic radiation;
- need to calibrate to correct for changes in cosmic radiation):
  - count growth rings in old trees (California bristlecone pines) (allows calibration up to 5000 years),
  - match growth pattern of dead wood (width of rings) with dated specimens extend calibration to about 7000 years
  - use U-238 and C-14 content in corals to cross-calibrate C-14 method with more reliable U-238 method (error on U-238 is only about 1%) extend applicability of (calibrated) C-14 method to about 30000 years (age corrections from calibration are up to about 15%).
- newest method: use mass spectrograph to count number of C-14 and C-12 atoms in sample (compare to number in living specimens);
  method needs much smaller samples, gives more precise results, works up to about 70000 years.

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Mon Nov 18 16:25:15 EST 1996