Lecture 09 Nuclear Physics Part 1 Structure and Size of the Nucleus Νuclear Masses Binding Energy The Strong Nuclear Force
Structure of the Nucleus Discovered by Rutherford, Geiger and Marsden in 1909 (see lecture ) Nucleus consists of protons and neutrons. Terinology: Refer to a nucleus with a given nubers of neutrons and protons as a A nuclide Z X ZAtoic Nuber (nuber of protons) NNeutron nuber (nuber of neutrons) AMass nuber Neutrons and protons are known as nucleons AZ+N (9.1)
Nuclear Size De Broglie wavelength of particle which becoes scattered gives approxiate size of object under investigation. Rutherford used α-particles of energy 7.7 MeV. What is the de Broglie wavelength of the α-particles? KE p λ p 4 1.66056 1.8 h p p 4 1.66056-19 kgs 6.63 1.8 34 19 1 7 5.18 7 7.7 15 7.7 6 6 1.60 1.60 19 19 First deterination of nuclear size around -14
Further scattering by electrons, protons and neutrons at varying energies gives nuclear radius R 1. A 1 3 f (9.) 1f -15 Volue V of a sphere R 3 V A Nucleons packed like olecules in a liquid drop!
Typical nuclear size -14, typical atoic size - The ato is as epty as the solar syste!
Nucleon Masses Masses expressed in ters of unified ass constant (u) C 1 Mass of ato defined to be exactly 1u 6 u 1.66056-7 MeV kg 931.5 Proton, neutron, electron asses: c p n e 7 MeV 1.6764 kg 0776u. 938.8 c 7 MeV 1.6750 kg 08665u. 939.57 c 31 MeV 9.9 kg 0.000549u 0.511 c
Atoic asses in the periodic table are weighted averages over different isotopes. Eg Chlorine isotopes with relative abundance: 35 17 Cl (75.4%) and 37 17 Atoic ass of Cl (4.6%) Chlorine 35u 0.754 + 37u 0.46 35.5u
Question What is the ass density of a typical nucleus, eg? 16 8 O Sphere Density More volue than ρ M V 14 4 3 4π 3 V R (1.) A 1.16 3 3 7 (16 u )(1.6606 ).3 43 1.16 ties the density of water! 17 43 kg 3-3
E E nucleons BE n H Atoic the c binding ass [ Z + N ] neutron ass and H of asses instead. (9.3) energy, difference the ass, neutral are The ass n Binding Energy Nuclear ass < Z proton ass + N BE of H ato easier to electron between to x X c the ass easure ass stable (9.4) of tal ass nucleus neutral than contributi of neutron Soe of the ass has been converted to energy needed to bind the nucleus together! the A Z X X ato, nuclear on cancels separated asses ass as so well. we use
Question (a) What is the binding energy of 6? (b) What is the binding energy per nucleon? 1 C
Binding Energy per Nucleon fusion fission Overall shape can be explained by fission and fusion (coing later!)
Copare Ionisation and Nuclear Binding Energies Most of the energy in the ato is bound in the nucleus!
Nuclear Energy Levels Fro quantu echanics of atos, we know that atos with Z,,18,36,54 are stable because sub-shells and shells are filled. Nucleons are also spin-1/ particles and are arranged in discrete energy levels. Values of Z or N of agic nubers:,8,0,8,50 lead to stable nuclei due to filled energy levels. Nuclei with agic Z and N are particularly stable eg: 4 He, 16 8 O, 40 0 Ca, 48 0 Ca and 08 8 Pb
Segré Chart >3000 known nuclei but < 300 stable 80 Z 40 40 80 10 Stable nuclei need a neutron excess to reduce effects of Coulob repulsion between protons
The Strong Nuclear Force Q) Why do the protons which ake up the nucleus not repel each other sufficiently to cause the nucleus to disintegrate? Where does the binding energy coe fro? A) There is another force at work in the nucleus and which is not apparent at larger distance scales : the strong nuclear force Q) Can we use our fundaental quantu echanics knowledge to find out about its properties? A) Yes! Easily!
Nucleons transit the strong force to each other through the exchange of another particle, the pion. pion nucleon nucleon Fro Heisenberg s Uncertainty principle, energy E can be Borrowed for a tie t, as long as Et > h. This allows the pion to be created and exist long enough to be exchanged.
Pion ass Aount of Tie of The force cannot be transitted at a speed M Range of energy borrowed interaction 135 MeV/ c force t c t h E 3.4 E.4 8-8 6.63-8 3.1 kg ( 8 3 ) > c 3 34 9 3.1 This explains why the strong force is not significant outside of the nucleus! A ore sophisticated approach gives the range at 6x -16, which is roughly the radius of a nucleon. The strong force acts on nucleons adjacent to each other! M c 15 3 s