bsc maths-ii

8/8/2019 Bsc Maths-II

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CONSTITUENTS

OF

NUCLEI


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Group membersGroup members

JINITHA MARY 4105JINITHA MARY 4105 AMALA JOSE 4114 AMALA JOSE 4114

LIGI JOB 4135LIGI JOB 4135


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The ProtonThe Proton--ElectronElectron

HypothesisHypothesis As early as 1816,on the basis of small number of atomic weight of elementsthen known,Prout suggested that all atomic weights being whole numbers,

they are integral multiples of the atomic weight of hydrogen and so all

elements must be built up of hydrogen. But as it was found that atomic

weights of some elements are fractional,Prouts hypothesis was

discarded.Still,since many elements have atomic weights which are veryclose to whole numbers, it seemed that there is some basis for Prouts

hypothesis. His suggestion received new support during the early years of

the 20th century when the study of the radioactive elements led to the

discovery of the isotopes. It was concluded that the atomic weights of the

elements become fractional due to the existence of two or more isotopes of

the elements. This led to formulate his whole number rule, which is really amodified form of Prouts hypothesis. The analysis of positive rays from

different substances revealed that the lightest positively charged particle

ever found had the same mass as the hydrogen atom, and carried unit

charge equal in magnitude to the electronic charge, but of opposite sign.


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This particle was confirmed to be the nucleus of the hydrogen atom,and it was found to have a massvery close to one atomic massesunit. The combination of the whole number rule and the properties ofthe hydrogen nucleus led to the conclusion that atomic nuclei arecomposed of hydrogen nuclei.The hydrogen nucleus was called theproton.

The atomic nucleus-the central massive core of the atom-wasdiscovered by Rutherford in 1911 through his alpha scatteringexperiments. The experimental skill of Marsden confirmed its

existence .According to them each atom consists of a very smallnucleus having radius of the order of 10-14.The discovery of thenucleus led to the Bohr model of the atom. However, in thesedevelopments, the nucleus was regarded just a point having positivecharge, located at the centre of the atom and all the importantproperties were attributed to the electron revolving round thenucleus. The studies on radioactivity revealed the very significant

role the nucleus has in the theory of the atom. The fact that inradioactivity atomic nuclei emit alpha and beta particles havingcorpuscular nature indicated that the nucleus has some constituentsinside. The constituents should have properties to enable them to bebound together inside the nucleus. Thus the nucleus should have adefinite structure.


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ATOMIC RADIUS VARIATION IN THE PERIODICATOMIC RADIUS VARIATION IN THE PERIODIC

TABLETABLE


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The fact that radioactive nuclei emit alpha particles led to the

speculation that in each nucleus there must be sufficient number ofthose particles. This idea was forced to be ruled out due to the

existence of the hydrogen nucleus, namely the proton. Then came

the next immediate suggestion that all nuclei are made up of

protons. If this is accepted, the mass number A and the atomic

number Z of a nucleus should be identical.However,with the only

exception of hydrogen, they are quite different for atomic nuclei. Toovercome this difficulty, the proton-electron model of the nucleus

was suggested. In this model, it was postulated that the nucleus with

mass number A and atomic number Z ,contained a protons and(A-Z)

electrons. With this theory, the charge of the nucleus is

A(+e)+(A-Z)(-e)=Ze.Thus the theory could explain the mass numberand the charge of the nucleus.


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The proto-electron hypothesis seemed to give satisfactoryexplanation for the emission of alpha and beta particles inradioactiveity.Beta particles are identical with the electrons. Thepresence of electrons in the nucleus make it seem reasonable thatunder appropriate conditions one of them may be ejected. It is alsoapparently reasonable to assume that an alpha particle may beformed inside the nucleus by the combination of four protons andtwo electrons. The alpha particle may exist as such inside thenucleus or may be formed at the instant of emission.

Though the hypothesis seemed to have some satisfactory aspects, ithad to be abandoned due to certain contradictions. The detailedstudy of spectral lines of certain elements revealed that the atomicnucleus has an angular momentum or nuclear spin with which isassociated a magnetic moment. The proton-electron hypothesis

could not satisfactorily explain these special features of the nucleus.The hypothesis also failed to account for the energy of the electron ifit were present in the nucleus. Developments in wave mechanicsconclusively established that electrons cannot be present in thenucleus. The problem could be solved with the discovery of theneutron by Chadwick in 1932.


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The ProtonThe Proton--Neutron HypothesisNeutron Hypothesis The discovery of the neutral particle,neutron,having mass equal to

unity led to the assumption that every atomic nucleus consists of

protons and neutrons. This proton-neutron hypothesis was used for

the first time by Heisenberg in 1932 as the basis of a detailed theory

of the nucleus. According to it, since the protons and neutrons haveunit mass, the total number of particles in the nucleus-protons plus

neutrons-is equal to the mass number A of the nucleus. The number

of protons is given by the atomic number Z.Therefore the number of

neutrons in the nucleus or the neutron number N=(A-Z).In the case

of many elements, the nuclei are found to contain the same number

of protons but different number of neutrons ie,they have the sameatomic number Z,but different mass numbers A. They are identical in

chemical properties since the properties depend on the atomic

number Z.such nuclei are called isotopes.


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Example: Hydrogen has three isotopes-ordinary hydrogen with Z=1and A=1,heavy hydrogen or deuterium with Z=1 and A==2 and

tritium with Z=1 and A=3.Similarly carbon has six isotopes, all with

atomic number 6 and mass numbers ranging from 11 to 16. In

naturally occurring carbon, they are present in different percentages.

These percentages are referred to as natural abundances.Artificialltisotopes may be produced by nuclear reactions.


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HYDROGEN ISOTOPESHYDROGEN ISOTOPES


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Isotopes of carbon


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The proton-neutron hypothesis satisfies the observations regardingnuclear angular momenta.The hypothesis also gives satisfactoryexplanation for radioacivity.Electrons can never be present in thenucleus due to various reasons. Still in radioactivity, which isessentially a nuclear disintegration process, beta particles which areidentical with the electrons are emitted. The explanation for this isthat the beta particles are created only in the act of emission andnever before. The emission is regarded as the result of the changeof a neutron in the nucleus into a proton with the emission of anelectron and a new particle called the neutrino. Both theoretical andexperimental evidence offer strong support to this view. Similarly analpha particle can be formed by the combination of two protons andtwo neutrons. They may combine and exist as an alpha particleinside the nucleus or it may be formed just at the moment of

emission. The latter possibility is considered more likely.


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