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Nuclear and Physics Module 1

By

Dr. Manjula Sharma Asstt. Prof. (Physics) Deptt. of Physical Sciences and Languages COBS, CSKHPKV, Palampur, HP-176062 Mail Id: [email protected] Contact no: 7018006656

DISCOVERY OF NUCLEUS discovered the nucleus of the in 1911.In 1911, Rutherford, Marsden and Geiger discovered the dense by bombarding a thin gold sheet with the alpha emitted by radium. Rutherford and his students then counted the number of sparks produced by these alpha particles on a zinc sulphate screen. From this observation, they concluded that almost all the atomic was concentrated in a tiny volume situated at the atome center, the atomic nucleus.

Constituents of Nuclei

1) Proton theory :- Before the discovery of by Chadwick in 1932, protons and electron were considered as the building blocks of the nucleus. According to this theory:- a) are emitted by radioactive nuclei in – decay process. b) From spectrum data it was found that of different nuclei were whole number multiple of and this hydrogen is named as proton. c) Since, atom is whole as neutral so it was considered that number of electrons and protons are same. FAILURES :- 1) WAVE MECHANICAL CONSIDERATION :- According to Heisenberg uncertainity principle Total momentum of electron inside the nucleus must be = 0.527 * 10-20Jsm-1 After this if rest mass energy is calculated then it is 10MeV , but we know rest mass energy is 3 to 4 MeV. So electons do not lie inside nucleus. 2) NUCLEAR :- According to this theory have half integral spin but experimentally it is integral. 3) NUCLEAR :- Magnetic moment of electrons is about 2000 times is more than protons so that is why electrons do not lie inside nucleus. 4) WAVELENGTH :- Wavelength of electron is larger than nuclear dimensions so electrons do not lie inside nucleus. 2) PROTON NEUTRON THEORY :- Electron proton theory failed due to properties of free electron . Further it was predicted that electron is bound with proton and it forms a new particle called NEUTRON. It was discovered by .

Facts in support of it :- 1) Wave mechanical consideration :- According to this momentum of proton = 0.527 * 10-20 Jsm-1 So total energy of proton is 940 MeV and experimentally it is 938 MeV. 2) Nuclear spin :- According to this spin will be integral or half integral is A(mass no.) is even or odd. 3) Nuclear magnetic moment :- Magnetic moment of neutron is same in magnitude but opposite in direction. 4) Finite size :- Since both protons and have same size so it is not difficult for nucleus to have neutrons in it. Properties :- 1) Nuclear size :- Experimentally, V ∝ A where, V = Volume of nucleus and R = Radius of nucleus 1/3 -15 R = R0A where R0 varies from 1.2 to 1.6 fermi (1 F = 10 ).

2) Nuclear shapes :- Quadrupole moment (Q) measures the departure of nucleus from its spherical symmetry . Q<0 OBLATE SHAPE , Q>0 PROLATE SHAPE AND Q =0 SPHERICALLY ELLIPSOIDAL . 3) :- 4) Nuclear mass :-

5) Nuclear charge :- 6) Nuclear Wave mechanical properties :- (a) P = +1; Parity is even or positive; P = -1; Parity is odd or negative. Parity is also related to orbital as, P = (-1)l (b) Statistics

In quantum mechanical treatment, a composite system with a group of particles such as a nucleus is described by either Bose- Einstein (B-E) or the Fermi-Dirac (F-D) Statistics.

Particles obeying F-D statistics are called Frmions (e.g. protons, neutrons, electrons) and the particles obeying B-E statistics are called ( e. g. , π-). 7) Angular momentum of Nucleus (I) :-

8) Magnetic moment of Nucleus (μI) :- Associated with each nuclear spin is a magnetic moment which is associated with the angular momentum of the nucleus. It is common practice to express these magnetic moments in terms of the nuclear spin in a manner parallel to the treatment of the magnetic moments of electron spin and electron orbital angular momentum. For the electron spin and orbital cases, the magnetic moments are expressed in terms of a unit called a which arises naturally in the treatment of quantized angular momentum.

9) Electric moment of Nucleus :- The nuclear electric quadrupole moment is a parameter which describes the effective shape of the ellipsoid of nuclear charge distribution. A non-zero quadrupole moment Q indicates that the charge distribution is not spherically symmetric. By convention, the value of Q is taken to be positive if the ellipsoid is prolate and negative if it is oblate. The quantity Q0 is the classical form of the calculation represents the departure from spherical symmetry in the rest frame of the nucleus. The expression for Q is the quantum mechanical form which takes takes into account the nuclear spin I and the projection K in the z-direction.

Mass Defect The that bind together in an atomic nucleus are much greater than those that bind an electron to an atom through electrostatic attraction. This is evident by the relative sizes of the atomic nucleus and the atom (10−15and 10−10 m, respectively). The energy required to pry a from the nucleus is therefore much larger than that required to remove (or ionize) an electron in an atom. In general, all nuclear changes involve large amounts of energy per particle undergoing the reaction.

Packing Fraction

The term packing fraction (f) is the mass defect per contained in the nucleus

where, ΔM = mass defect M = Actual mass of an element in a. m. u. A = Mass no. i. e. number of protons plus neutrons in the nucleus.

Binding Energy The energy equivalent to mass defect (△m) in a nucleus is the energy needed to hold or bind the nucleons together inside the nucleus. This energy, called of nucleus. It is the measure of the stability of the nucleus. Clearly binding energy of the nucleus will be equal to the total energy released when the nucleons combine to form the nucleus. Thus binding energy is also defined as the energy required to break up a nucleus into its constituent protons and neutrons and to keep them at rest at infinite distances from each other. Therefore work equal to the binding energy must be done to split the nucleus completely into its constituent nucleons.

Binding energy is expressed as : B = △mc2 2 B = [ZMP+ (A-Z)Mn – Mnucleus]c So mass defect appears as binding energy.

Binding energy per nucleon:- The average energy required to extract one nucleon from the nucleus is called binding energy per nucleon.

Binding energy determines the stability. If binding energy per nucleon is small, the nucleus is less stable whereas binding energy per nucleon is more then nucleus is more stable. Therefore heavy nuclei are less stable then lighter nuclei. If we plot a graph between the binding energy per nucleon and mass no. the graph is shown as:

Binding energy per nucleon curve From the curve the conclusions are drawn:

1 2 3 1)Binding energy per nucleon of light nuclei like 1H , 1H , 1H etc. is low. 2)For ranging from 2 to 20 there are sharply defined peaks corresponding to 4 8 12 16 20 2He ,4Be , 6C , 8O , 10Ne . These peaks indicate that these nuclei are most stable then the other nuclei in their neighbourhood. 3)It has a broad maximum to value of 8.5 Mev/nucleon in the mass, ranging from 40 to 140. It 56 has a peak value of 8.8 Mev/nucleon for 26Fe . It is the most stable nucleus, since the highest maximum energy required to pull a nucleon away from it. 4)For mass number more than 56, the binding energy per nucleon decreases slowly and is least 234 value for 92U is 7.6 Mev. 5)Binding energy per nucleon for lighter and heavier nuclei are less and they are less stable than middle one. In order to attain stability the heavier nucleon may split into lighter nuclei(by process of ) and lighter nuclei may unite together to form heavier nucleus (by ).In both the processes large amount of energy is released. 6) For the having A<28 there exists cyclic recurrence of peaks. These peaks corresponds to those nuclei whose mass are multiple of four and contain equal number of protons and neutrons. 4 8 12 16 20 So the binding energy of 2He , 4Be , 6C , 8O , 10Ne are greater than those of their neighbours. Thus these nuclei are more stable . further it is noted that similar but less prominent peaks are observed at the values of Z and N equal to 20,28,50,82 and 126. These numbers are called magic numbers. Average binding energy for light nuclei (A<28) Nuclear Stability

Certain Nuclei/ are more stable than others. Their stability is determined by the ratio of the number of neutrons to the number of protons in the nucleus. At low atomic masses, the stable ratio is approximately 1:1. At about an number of 20 this starts to increase until it is around 1.5:1 for the very heavy elements. This is due to the fact that with higher numbers of protons more neutrons are needed due to the repulsion of the protons from .

1:1 is stable only below Z=20 and that after that the stable nuclei become neutron rich. This ratio is not exact but represents a "band of stability" around which unstable isotopes cluster. There are a large number of unstable isotopes both above the band (too high a number of neutrons) and below the band (too high a number of protons).

At some point there are no longer any stable isotopes regardless of the neutron to proton ratio. This can be seen at very high atomic numbers. Above mass 208 there are no stable isotopes. The graph below shows a number of isotopes along with a line with the 1:1 ratio. The stable isotopes are plotted as black dots. The unstable isotopes are plotted with a color coding based on their most prominent decay route. Note that isotopes that are closest to the stable isotopes in the center are "more stable" than isotopes that are father away. This "band" of isotropes running down the center of the plot is the "band of stability".

The nucleus is unstable if the neutron-proton ratio is less than 1:1 or greater than 1.5. At close distances, a strong nuclear exists between nucleons. This attractive force comes from the neutrons. More protons in the nucleus need more neutrons to bind the nucleus together. The graph below is a plot of the number of neutrons versus the number of protons in various stable isotopes. The stable nuclei are in the pink band known as the belt of stability. They have a neutron/proton ratio between 1:1 and 1.5. As the nucleus gets bigger, the electrostatic repulsions between the protons gets weaker. The nuclear strong force is about 100 times as strong as the electrostatic repulsions. It operates over only short distances. After a certain size, the strong force is not able to hold the nucleus together. Adding extra neutrons increases the space between the protons. This decreases their repulsions but, if there are too many neutrons, the nucleus is again out of balance and decays. For proton numbers(Z) up to 20, N=Z is a straight line.

For all nuclei with Z>20 , stable nuclei have more neutrons than protons, the line curves upwards.

Unstable nuclei above the stability curve are called neutron-rich.

Unstable nuclei below the stability curve are called neutron-poor.