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Nucleus Chapter

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Published in: AIEEE | Physics
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Nucleus Chap- Notes On Important Class XII NCERT Topics.

Akhilesh K / Lucknow

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  1. CHAPTER 13 - NUCLEI - PHYSICS NOTES BY Akhil Scattering of alpha particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about 104. This means volume of a nucleus is about 10 12times the volume of the atom. Atomic mass unit (u), defined as l/ 12th of the mass of the carbon (12C) atom. Isotopes- Atomic species of the same element differing in mass are called isotopes.(same z, different A) Isobars — same atomic mass A, but different atomic number Z. Isotones- atomic species have same number of neutrons but different atomic number Z. Number of protons in the nucleus of the atom is Z, the atomic number. v/ No. of proton = no. of electron v/ Mass number A = Z+N , N is no.of neutron & Z is no. of proton in nucleus. Discovery of Neutron- Discovered by James Chadwick, who observed emission of neutral radiation when beryllium nuclei were bombard with alpha particles (u particles are helium nuclei). These neutral radiations consists of a new type of neutral particles called neutrons. Mass of a neutron 1.00866 u = kg. radius R= ROA1/3 SIZE OF THE NUCLEUS - nucleus of mass number A has a 1.2 x 10 15 m. This means the volume of the nucleus is proportional to R3 which is proportional to A. Thus the density of nucleus is a constant, independent of A, for all nuclei. E=mc2 Mass — Energy - Einstein gave the famous mass-energy equivalence relation, Nuclear binding energy- nucleus is made up of neutrons and protons. Therefore it may be expected that the mass of the nucleus is equal to the total mass of its individual protons and neutrons. However, the nuclear mass M is found to be always less than from its constituents mass. Mass defect (AM ) - difference in mass of a nucleus and its constituents is called Mass defect. AM = [ zmp + Binding energy- AM.c2 If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy Eb released in the process is called Binding energy of the nucleus. If we separate a nucleus into its nucleons, we have to supply a total energy equal to Eb to those particles. Binding energy per nucleon, (Elm) is the ratio of the binding energy (Eb) of a nucleus to the number of the Ebn= Eb/ A nucleons (A). Binding energy per nucleon as the average energy per nucleon needed to separate a nucleus into its individual nucleons. 10 8 6 4 2 o o 32s IGO e 50 1 cro 100 1 150 u 97 200 gas 250 Mass nunuber (A)
  2. (i) (ii) Binding energy per nucleon, is practically constant, i.e. practically independent of the atomic number for nuclei of middle mass number ( 30 < A < 170). Binding energy is lower for both light nuclei A coulomb force > gravitational force. The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometres. This leads to saturation of forces in a medium or a large-sized nucleus, which is the reason for the constancy of the binding energy per nucleon. v/ Potential energy is a minimum at distance 0.8 fm. v/ Force is attractive for r > ro , v/ force is repulsive if r < ro The nuclear force between neutron-neutron, proton-neutron and proton-proton is approximately the same. The nuclear force does not depend on the electric charge. RADIOACTIVITY- o 10b 1 2 r (fin) 3 A. H. Becquerel discovered radioactivity in 1896. Radioactivity was a nuclear phenomenon in which an unstable nucleus undergoes a decay. This is referred to as radioactive decay. Three types of radioactive decay occur in nature. (i) a-decay in which a helium nucleus 4He is emitted; (ii) ß-decay in which electrons or positrons (particles with the same mass as electrons, but with a charge exactly opposite to that of electron) are emitted; (iii) y-decay in which high energy (hundreds of kev or more) photons are emitted. Law of radioactive decay- In any radioactive sample, number of nuclei undergoing the decay is proportional to the total number of nuclei in the sample (N). (a, or y ) per unit time AN AN = IN, Where 1 is called radioactive decay constant. — ocN, AT -IN = AT AN After integration , we get law of radioactive decay AT R=Roe It On solving this equation we get, Rate decay, R= —
  3. ACTIVITY- total decay rate R of a sample of one or more radionuclides is called Activity of that sample. The SI unit for activity is Becquerel (Bq). 1 Bq= Idecay/sec. 1 curie = 1 Ci = 3.7 x 1010 Bq (decays per second). Half-life Tl/2 of a radionuclide, the time at which both N and R have been reduced to one-half their initial values. ln2 0.693 TIE = 1 1 1 Average life or mean life, T = 1 Alpha decay- When a nucleus undergoes alpha decay it transforms to a different nucleus by emitting an alpha-particle. Transformation of a parent nucleus X into a daughter nucleus Y zX 4 _{Y+ 2He Alpha-decay of U can occur spontaneously (without an external source of energy) because the total mass of the decay products Th and He is less than the mass of the original U. Thus, the total mass energy of the decay products is less than the mass energy of the original nuclide. Difference between the initial mass energy and the final mass energy of the decay products is Q= (mx-my-mHe)c2 called Q value or disintegration energy of alpha decay, Beta decay- A nucleus that decays spontaneously by emitting an electron or a positron is said to undergo ß decay. In beta-minus decay, a neutron transforms into a proton within the nucleus hence an electron is emitted by the nucleus. 32 In beta-plus (ß+)decay, a proton transforms into neutron (inside the nucleus) hence positron is emitted by the nucleus. p 71 + e + + v 22 22 IINa * 10Ne + e+ + v symbols and v represent antineutrino and neutrino, respectively; both are neutral particles, with very little or no mass. Gamma decay- There are energy levels in a nucleus, just like there are energy levels in atoms. When a nucleus is in an excited state, it can make a transition to a lower energy state by the emission of electromagnetic radiation. As the energy differences between levels in a nucleus are of the order of MeV, the photons emitted by the nuclei have MeV energies are called gamma rays. Radionuclides after an alpha decay or a beta decay leave the daughter nucleus in an excited state. The daughter nucleus reaches the ground state by a single transition or sometimes by successive transitions by emitting one or more gamma rays. Co 27 1.17MeV F; = 1.33 MeV 60 28
  4. Nuclear Fission- Enrico Fermi found that when neutrons bombard various elements, new radioactive elements are produced. When a neutron was bombard on a uranium target, the uranium nucleus broke into two nearly equal fragments releasing great amount of energy. The fragment nuclei produced in fission are highly neutron-rich and unstable. They are radioactive and emit beta particles in succession until each reaches a stable. Examples are o n + U 25326 U + + 4 Ion 140 n + 29325 U Nuclear fusion- Xe + 38Sr + 2 Energy released if two light nuclei combine to form a single larger nucleus, process called nuclear fusion. IH+ v+ 0.42 Mev IH+ IH+3He+ n + 3.27 Mev 31H+ {H + 4.03 MeV Fusion reaction in the sun is a multi-step process in which hydrogen is burnt into helium, hydrogen being the 'fuel' and helium the 'ashes'. The proton- proton (p-p) cycle by which this occurs, represented by the following sets of reactions: H + 21 H + + v + 0.42 211-1 + {H + Y + 5.49 MeV 2 H + *He+ 11 H + {H + 12.86 MeV (ii) (iii) (iv) For the fourth reaction to occur, the first three reactions must occur twice, in which case two light helium nuclei unite to form ordinary helium or nucleus. If we consider the combination 2(i) + 2(ii) + 2(iii) +(iv), the net effect is 411H+2e + 24He+2v+6y+26.7MeV or (41H+ Thus, four hydrogen atoms combine to form an Helium atom with a release of 26.7 MeV of energy.

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