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PHY206: Nuclear Forces, Mass Defect, Binding Energy, Radioactivity & Decay Law – Complete Notes

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PHY206: Nuclear Forces, Mass Defect, Binding Energy & Radioactivity Notes

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The atom
In 1904, Thomson considered atomic structure to be represented by a ‘plum pudding’ in so far as the atom
was made up of negatively charged electrons surrounded by a soup of positive charge to keep the overall
charge neutral.


Rutherford and the planetary system of the atom
Atoms are electrically neutral, so if they contain electrons they must also contain some positive charge, but
where? Thomson assumed that this was uniformly distributed like a soup throughout the atom but this was
only conjecture. To find out, in 1909 Rutherford fired positively charged helium (He2+) ions withhigh energy
at gold atoms in a thin gold film. Based on the theory that positive and negative charges were spread evenly
within the atom and that therefore only weak electric forces would be exerted on the high energy ions passing
through the thin foil, he expected to find that most of the ions travelled straight through the foil with little
deviation.
What he found, to great surprise, was that whilst most passed straight through the foil, a small percentage
(about 1 in 10000) were deflected at very large angles and some even bounced back toward the ion source.
Because helium ions are about 8000 times the mass of an electron and impacted the foil at very high
velocities, it was clear that very strong forces were necessary to deflect these particles. (Imagine firing bullets
at soup. Even if just one ricocheted back it would be surprising!!)




The He2+ positive ions had clearly been repelled by an incredibly large positive charge within the atom,
this charge concentrated in a dense region also containing most of the mass. This work led in 1913 to
Rutherford declaring theatom to contain a very small nucleus of high positive charge (equal to the number
of electrons in order to maintain neutrality) and to be similar to the ‘solar-system-like’ model, in which
a positively charged nucleus is surroundedby an equal number of electrons in orbital shells.
From purely energetic considerations of how far helium ions of positive charge and known velocity
would be able to penetrate toward the central positive charge of the gold nucleus, Rutherford was able to
1

, calculate that the radius of the gold nucleus would need to be less than 3.4 x 10-14 metres (the modern
value is only about a fifth of this). The radius of the entire gold atom was known at the time from
diffraction measurements to be 10-10 metres or so. This then implied that the diameter of the nucleus,
containing all the positive charge and almost all of the mass, was less than 1/3000 th the diameter of the
atom.
Detailed analysis of scattering data for various elements has since found the diameter of the nucleus to
range from 2 to 9 × 10-15 m from hydrogen to uranium, and the diameter of the nucleus to be almost 10-5
the diameter of the atom. We now also know the nucleus contains both protons (positively charged) and
neutrons (electrically neutral) particles of almost the same mass. Scientists at this time had no idea about
the existence of neutrons.


Nuclear Composition
 Atomic nuclei are build up of protons and neutrons.
 Nucleus of hydrogen atom contains only single proton.
 Charge on a proton is +1.6x10-19 C and its mass is 1836 times greater than that of electron.
 Neutrons are uncharged particles and mass of a neutron is slightly greater then that of a proton.
 Neutrons and protons are jointly called nucleons.
 Number of protons in nuclei of an element is equal to the number of electrons in neutral atom of that
element.
 All nuclei of a given element does not have equal number of neutrons for example99.9 percent of
hydrogen nuclei contains only one proton , some contain one proton and one neutron and a very little
fraction contains one proton and two neutrons.
 Elements that have same number of protons but differ in number of neutrons in their nucleus are called
ISOTOPES.
 Hydrogen isotope deuterium is stable but tritium is radioactive and it decays to changes into an isotope
of helium.

 In heavy water instead of ordinary hydrogen deuterium combines with oxygen.
 Symbol for nuclear species follows the pattern AXZ where
X= Chemical symbol of element
Z= Atomic number of element or number of protons in the nucleus of that element.
A= Mass number of nuclide or number of nucleons in the nucleus. A=Z+N where N is the
number of neutrons in the nucleus.
 In symbolic form
(1) hydrogen = 1H1 and Deuterium = 2H1
(2) Chlorine isotopes are 35Cl17 and 37Cl17
 Atomic masses refer to the masses of neutral atoms , not of bare nuclei i.e., an atomic mass always
includes the masses of all its electrons.
 Atomic masses are expressed in mass units (u).
 One atomic mass unit is defined as one twelfth part of the mass of 12C6 atom.
 So the mass of 12C6, the most abundant isotope of carbon is 12u.
 Value of a mass unit is
1u=1.66054x10-27Kg
 Mass of proton is 1.00727663 u which is equal to 1.6725 x 10-27kg or 938.26 MeV.
 Mass of neutron is 1.0086654 u which is equal to 1.6748 x 10-27kg or 939.55 MeV.

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