shell model and ionization chamber

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2. Shell Model
 The shell model of the nucleus assumes that the energy structure (energy
 levels of the nucleons) of the nucleus is similar to that of an electron shell in an atom.
 According to this model, the protons and neutrons are grouped in shells in the nucleus,
similar to extra-nuclear electrons in various shells outside the nucleus.
 The shells are regarded as “filled” when they contain a specific number of protons or
neutrons or both.
 The number of nucleons in each shell is limited by the Pauli exclusion principle.
 The shell model is sometimes referred to as the independent particle model because it
assumes that each nucleon moves independently of all the other nucleons and is acted
on by an average nuclear field produced by the action of all the other nucleons.

3. salient features of shell model
• It is known that a nucleus is stable if it has a certain
definite number of either protons or neutrons.
• These numbers are known as magic numbers.
• The magic numbers are 2, 8, 20, 50, 82 and 126.
• Thus nuclei containing 2, 8, 20, 50, 82 and 126
nucleons of the same kind form some sort of closed
nuclear shell structures.

4. salient features of shell model
• The inert gases with closed electron shells exhibit a high degree of chemical stability.
Similarly, nuclides whose nuclei contain a magic number of nucleons of the same kind exhibit
more than average stability.
• Isotopes of elements having an isotopic abundance greater than 60% belong to the magic
number category.
• Tin (50Sn) has ten stable isotopes, while calcium (20Ca40) has six stable isotopes. So elements
with Z = 50, 20 are more than usually stable.
• The three main radioactive series (viz., the uranium series, actinium series and thorium
series) decay to 82Pb208 with Z = 82 and N = 126. Thus lead 82Pb208 is the most stable isotope.
This again shows that the numbers 82 and 126 indicate stability.
• It has been found that nuclei having a number of neutrons equal to the magic number,
cannot capture a neutron because the shells are closed and they cannot contain an extra
neutron.

5. • It is found that some isotopes are spontaneous neutron emitters when
excited above the nucleon binding energy by a preceding β-decay.
• These are 8O17, 36Kr87 and 54Xe137 for which N = 9, 51 and 83 which can be
written as 8 + 1, 50 +1, and 82 + 1. If we interpret this loosely bound
neutron, as a valency neutron, the neutron numbers 8, 50, 82 represent
greater stability than other neutron numbers.
• Each nucleon shell has a specific maximum capacity. When the shells are
filled to capacity, they give rise to particular numbers (the magic numbers)
characteristic of unusual stability.
salient features of shell model

6. The shell model - magic numbers
• It is observed that even-even nuclei are, in general, more stable than odd-
odd nuclei. This is obvious from the shell model.
• According to Pauli’s principle, a single energy sublevel can have a
maximum of two nucleons (one with spin up and other with spin down).
• Therefore, in an even even nucleus only completed sublevels are present
which means greater stability.
• On the other hand, an odd-odd nucleus contains incomplete sublevels for
both kinds of nucleon which means lesser stability.

7.  The principle employed here is that charged subatomic particles can ionise gases.
 The number of ion-pairs produced gives us information not only on the nature of
the incident particles, but even on their energy.
 The ionisation chamber consists of a hollow metallic cylinder C, closed at both
ends, with a window W at an end for the entry of the ionising particles or
radiation.
 A metal rod R, well insulated from the cylinder, is mounted coaxially within the
cylinder.
 R is connected to a quadrant electrometer E. A p.d. of several hundred volts is
maintained between C and R.
 An earthed guard ring G prevents leakage of charge from the cylinder to the rod.
Ionization Chamber

8. Ionization Chamber

9. An ionisation chamber is much less
sensitive to β-particles (in comparison to
α-particles) because β-particles produce
fewer pairs of ions in their passage
through the chamber. Ionization
Chamber.
For detecting γ-rays, an ionisation
chamber of thick wall made of high
atomic-number material (Pt, Bi) is
employed. The γ-rays impinging on the
walls of the chamber eject high-speed
electrons which produce ionisation in the
gas