Properties of the nucleus. 9.1 Nuclear Physics. Isotopes. Stable Nuclei. Size of the nucleus. Size of the nucleus

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Properties of the nucleus 9. Nuclear Physics Properties of nuclei Binding Energy Radioactive decay Natural radioactivity Consists of protons and neutrons Z = no. of protons (tomic number) N = no.

1 Properties of the nucleus 9. Nuclear Physics Properties of nuclei Binding Energy Radioactive decay Natural radioactivity Consists of protons and neutrons Z = no. of protons (tomic number) N = no. of neutrons (Neutron number) = Z+N (Mass number) Notation :For element X with mass no. and tomic no. Z X Z Example He Isotopes Isotopes are nuclei that have the same no. of protons but different no. of neutrons. Plot of N vs Z for stable nuclei Stable Nuclei Unstable Nuclei The chemical properties are the same but the nuclear properties are different. i.e. some isotopes may be unstable and are radioactive. Outline shows unstable nuclei eg. H H 3 H Hydrogen - stable Deuterium - stable Tritium - radioactive Some radioactive nuclei 6 C 3 5 P 3 53 I N 38 9 U Z Max Z=83 Size of the nucleus From scattering experiments with alpha particles He ++ Size of the nucleus Radius varies as the cube root of r= r o /3 Closest approach KE PE =kq q /r For gold nuclei closest r < 3x0 - m This is smaller than the size of atoms r ~ 0-0 m where r o =.x0-5 m example For Uranium 38, = U 5 / 3 5 r.x0 = (38 ) = 7.x0 m

2 Forces in the nuclei Coulomb forces The protons repel each other with Coulomb forces. These are enormously large due to the small size. Nuclear forces +Z Equivalence of mass and energy famous result from Einstein s Special Relativity Theory E= mc mass can be converted into energy Energy equivalent of an electron mass The nucleus is held together by the nuclear force. This force acts only at short range (~0-5 m) and is independent of charge (i.e. acts between proton-proton, proton-neutron and neutron-neutron). E=mc = (9.x0-3 kg)(3x0 8 m/s) = 8.x0 - J =5.x0 5 ev= 0.5MeV n electron can be annihilated (converted completely to energy). 0.5 MeV photon is produced. Mass changes when energy is lost or gained Gasoline + O -> CO +water + kinetic energy (heat) Σmc + ΣEnergy =constant The energy released is equal to the change in mass in the reaction. E= mc CO + water is lighter. Burning kg of gasoline releases x0 6 J of energy. The change in mass is 6 E x0 J 0 m= = = 5x0 kg small change 8 c (3x0 m/s) in mass Binding energy The binding energy of the nucleus can be determined by measuring the mass of the components and the final product. Binding E= mc energy + Energy p + n -> D distance m = mass (hydrogen atom) + mass (neutron) mass (deuterium atom) m =.00785u u -.00u=.39x0-3 u u= x0-7 kg (atomic mass unit) E= mc = (.39x0-3 u)(.66x0-7 kg/u)(3x0 8 m/s) =3.6x0-3 J E=.x0 6 ev =. MeV Binding energy of the deuteron E Binding energy per nucleon (E/) N neutrons+ Z protons -> tom + energy Binding energy per nucleon (E/) fission fusion average no. of nuclear contacts increases favor higher average no. of contacts constant. Electrostatic forces favor lower Goes through a maxima at 56 Fe Goes through a maxima at 56 Fe Fusion (combine small nuclei) increases binding energy Fission (break large nuclei) increases binding energy

3 Radioactivity Decay process Unstable nuclei decay releasing energy and radiation. lpha decay Three types of radiation alpha (α) particles - He nuclei (+ charge) beta (β) particles - electrons (- charge) gamma (γ) particles - high frequency electromagnetic Increasing penetration radiation. (uncharged) Uranium decay Z X Z Y+ 3 9 U 90Th+ 38 He He Beta Decay Beta decay electron e - positron e + Z X Y + e + γ Z+ X Y + e + γ + Z Z e + positron has the same mass as an electron but a positive charge. the antiparticle of the electron γ neutrino, no charge, low mass particle carries of some momentum and energy γ anti-neutrino, antiparticle of the neutrino electron positron 6 C N 7 + e γ + N N + e + γ Gamma Decay Many nuclear reaction produce nuclear excited states that decay giving of high energy electromagnetic radiation-gamma rays. 60 Co Ni + e + γ + gamma(.7mev,.33mev) Radiation Penetration depth alpha particles Stopped by a sheet of paper beta particles - Stopped by a mm of aluminum gamma particles - Stopped by a few cm of lead 3

Measuring radiation Geiger Counter Natural radioactivity Many elements found in nature are unstable and decay emitting radioactivity. radiation These include Uranium, 38 U, Radon Ra and Potassium 0 K.

Cosmic rays Cosmic rays High energy particles (protons, alpha particles, atomic nuclei) from distant stars collide with atoms in the atmosphere and break them apart to sub atomic particles.

4 Measuring radiation Geiger Counter Natural radioactivity Many elements found in nature are unstable and decay emitting radioactivity. radiation These include Uranium, 38 U, Radon Ra and Potassium 0 K. Carbon C, ionization of gas causes current flow. Natural radioactive decay Thorium decay gives a variety of unstable products. Cosmic rays Cosmic rays High energy particles (protons, alpha particles, atomic nuclei) from distant stars collide with atoms in the atmosphere and break them apart to sub atomic particles. Some particles e.g. muons rain down to the earth s surface and are a source of background radiation. Cloud chamber cloud chamber can be used to visualize radioactive particles. The chamber contains a supersaturated vapor Cloud chamber demo UqLmQ radioactive source track The radioactive particle causes ionization of atoms The charge initiates the condensation of the vapor, Leaving a visible track.

5 Decay rate The rate of decay, R, for N nuclei is proportional to N N R = = λn t λ = decay constant (units time - ) ctivity (measure of the rate of radioactive decay) Units Curie, Ci = 3.7x0 0 Decays/s Radioactive decay Radioactive decay is a random process the amount of material remaining varies exponentially with time. t N= N e λ o Decay constant λ ( units /time) This can also be expressed as Half Life = N No t/t ln T = = λ λ Example 9.3 The half life of radium Ra is.6x0 3 yr. If the sample contains 3.00x0 6 nuclei. Find the activity in curies. (Ci=3.7x0 0 decays/s) ln T = = λ λ λ= = 3 T/.6x0 yr(365day / yr)(hr / day)(3600s /hr) =.37x0 s R=λN R=.37x0 - s - (3.00x0 6 nuclei) =.x0 5 decays/s R=.x0-5 Ci or µcuries 3.7x0 0 decays/sci Example 9.3 The half life of radium Ra is.6x0 3 yr. If the sample contains 3.00x0 6 nuclei. Find the number of nuclei after.8x0 3 yr. t/t / N= No 3 3.8x0 /.6x0 6 N= 3.00x0 N=3.00x0 6 (/8)=3.75x0 5 nuclei Example 9.3 The half life of radium Ra is.6x0 3 yr. If the sample contains 3.00x0 6 nuclei. Find the activity after.8x0 3 yr. R=λN fter this time since the no. of nuclei is reduced by a factor of 8 the decay rate will also be reduced by a factor of 8. Radioactive dating C is continually formed by cosmic rays in the upper atmosphere. n + N -> C + p so that the concentration of C is relatively constant over long times ( longer than the half life). C C decays T // = 5730 years R = µci/8 =. µci The fraction of C decays exponentially with time. 5

Ionization of air by a radioactive source produces a current. Smoke traps the electrons and reduces the current. setting off the alarm. Smoke Detector Medical pplications.

Reactive chemicals cause radiation damage to biological systems often reaction with DN Radiation Therapy Radioimmunotherapy Radiation is often used in treating cancer.

07 days Beta particle maximum energy- 807 kev average energy - 8 kev Range in tissue -.

6 Ionization of air by a radioactive source produces a current. Smoke traps the electrons and reduces the current. setting off the alarm. Smoke Detector Medical pplications. Radiation Damage. Nuclear particles have much higher energies than chemical bonds. Radiation breaks chemical bonds forming reactive chemical species radicals. Reactive chemicals cause radiation damage to biological systems often reaction with DN Radiation Therapy Radioimmunotherapy Radiation is often used in treating cancer. New methods for can deliver radiation more specifically to target cells external radiation Treatment of non-hodgkins lymphoma with radioimmunotherapy Iodine 3 Half-life 8.07 days Beta particle maximum energy- 807 kev average energy - 8 kev Range in tissue -. mm Properties of 3 I Common clinical applications Radioimmunotherapy, thyroid ablation for benign and malignant disease Medical Imaging X-ray Computer axial tomography (CT) Positron emission tomography (PET) Magnetic resonance imaging (MRI) Contrast Resolution. 6

CT scan Computer tomography Contrast x-ray absorption may use heavy elements to increase contrast i.

detector 3 detector at each detector absorbance is due to the sum of the absorptions from each segment.

Positron Emission Tomography Emission of gamma ray photons traveling in opposite direction by Positron-Electron annihilation.

7 CT scan Computer tomography Contrast x-ray absorption may use heavy elements to increase contrast i.e I, Ba incident x-ray c a b d detector detector three- dimensional image is reconstructed from many two dimensional pictures. detector 3 detector at each detector absorbance is due to the sum of the absorptions from each segment. (detector) = i + j For detectors -> linear equations Solve for and segment - > unknowns each absorbance CT scan of a chest Positron Emission Tomography Emission of gamma ray photons traveling in opposite direction by Positron-Electron annihilation. (conservation of momentum) Positrons are produced by decay of short lived radioactive nuclei such as 8 F (T / =0 min) F O+ e + +ν e nnihilation produces 0.5 MeV photons + e γ+γ + hf hf PET imaging system PET scan of the human brain Two coincident detectors are used to detect the gamma rays. The source is in a line directly between the two detectors. 5 O ( T / = min) marks the consumption of O due to brain activity. 7

Properties of the nucleus. 8.2 Nuclear Physics. Isotopes. Stable Nuclei. Size of the nucleus. Size of the nucleus

Properties of the nucleus. 8.2 Nuclear Physics. Isotopes. Stable Nuclei. Size of the nucleus. Size of the nucleus Properties of the nucleus 8. Nuclear Physics Properties of nuclei Binding Energy Radioactive decay Natural radioactivity Consists of protons and neutrons Z = no. of protons (Atomic number) N = no. of neutrons