Shell Model

The nuclear shell model is a model of the atomic nucleus. It uses the Pauli exclusion principle to explain the nucleus structure in terms of energy levels. In order to study the complete nucleus structure, various nuclear shell models were proposed. The first shell model was introduced in the year 1932 by Dmitry Ivanenko and later on developed by various physicists – Maria Goeppert Mayer, Eugene Paul Wigner, and J.Hans.D. Jensen in the year 1949.

Nuclear Shell Model

It basically explains the distribution of energy level into different atom shells and nucleus atom shells. A shell is described as the energy level where particles having the same energy exists. In this model, all the nuclear particles are paired one-to-one, neutron with neutron and proton with a proton. The paired neutrons and protons in nuclear energy levels are filled when the number of neutrons or protons is equal to 2, 8,20,28,50,82 or 126. These are the magic numbers which show the most stable nuclei.

Shell Model

The unpaired ones are responsible for the properties of a nucleus and valence electrons are responsible for different chemical properties of elements. With the help of the shell model, we can accurately predict the properties of nuclei such as angular momentum. But, for nuclei which are in a highly unstable state, the shell model needs to be modified or replaced with other models such as the collective model, liquid-drop model and compound nucleus model.

Shell Model of the Atom

It explains the arrangement of different electrons present around the nucleus of an atom as per energy levels.

Shell Model of the Atom

Shell Model of the Atom

Atomic Number = Number of electrons in an atom
  • Maximum number of electrons in the outer shell is 8 for neo atom,
  • Maximum number of electrons in the inner shells is 2n2, where n= shell number
Shell number, n 1 2 3 4 5
Maximum number of electrons in shell, 2n2 1 2 3 4 5

Atomic Shell Model explains the arrangement of electrons in an atom. When nucleons are added to a nucleus, binding of the energy is relatively less than the last one at certain points.  The origin of the shell model comes with different magic numbers of nucleons – 2,8,20,28,50,82,126 which are bounded tightly than the next higher number.

Difference Between Shell Structure of Nuclei and Shell Structure of Atom

Shell Structure of Nuclei
Shell Structure of Atom
Energy Level starts from Zero state Energy Level starts from the first state.
Magic Numbers,  Z= 2,8,20,28,50,82,126 and so on. Magic Numbers, Z = 2,10,18,36,54,86 and so on.
The average potential of Nuclei is different from that of an atom Average Potential varies.
Particles of the shell structure of nuclei are neutrons and protons Particles of the shell structure of atom are electrons.

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Practise This Question

A bob of mass m is suspended from the ceiling of a train moving with an acceleration a as shown in figure. Find the angle θ in equilibrium position.