Probing the Subatomic World •Nucleus consists of protons and neutrons. This explains the existence of isotopes, isobars, isotones, isomers and mirror nuclei.

The nucleus: A M Z , e.g. 14 C 6 Z = atomic number, # of protons/electrons A = atomic mass, total # of nucleons N = A – Z = number of neutrons

ISOTOPES ISOBARS – nuclides with identical Z – nuclides with identical A ISOTONES – nuclides with identical N ISOMERS – two nuclei of the same species but different energy states, of which at least one is metastable MIRROR NUCLEI – proton (neutron) number of one is the neutron (proton) number of the other Which are isotopes, isobars, isotones, mirror nuclei?

12 B 5 , 14 C 6 , 14 N 7 , 14 O 8 , 16 O 8

Isotopes 14 O 8 , 16 O 8 Isobars 14 C 6 , 14 N 7 , 14 O 8 Isotones 12 B 5 , 14 N 7 Isomers 14 O 8 , 16 O 8 Mirror nuclei 14 C 6 , 14 O 8

NUCLEAR SIZE (R. Hofstadter) –mean electromagnetic radius, i.e. the radius to the 50% point in the density distribution R e = (1.07  0.02) A 1/3 x 10 -15 m = 1.07 A 1/3 F 1 F (fermi) = 10 -15 m What is the mass number of a nucleus having a radius one third that of 27 Al 13 ?

 Discovery of radioactivity  Becquerel – uranium   M. Curie – polonium and radium Debierne and Giesel – actinium O. Hahn – radiothorium, mesothorium •Radioactive emissions o alpha particles – helium nucleus o beta particles – fast electrons o gamma rays – em radiation with wavelengths greater than X-rays

Radioactivity  - decay :helium nucleus is emitted from radioactive nuclide, leaving latter with two units less charge and four units less mass number (Z,A)  (Z – 2, A – 4) + 2 He 4  - decay: a negative electron is emitted, leaving the nucleus with one unit more charge and the same mass number (Z,A)  (Z + 1, A) +   -decay: an electromagnetic quantum is emitted, leaving the charge and mass number of the nucleus unchanged (Z,A)*  (Z, A) + h  How to test whether  ,  ,  ?

   x x – B-field source

Geiger counter- measures radioactivity Units: Curie (Cu) – quantity of any radioactive material giving 3.7 x 10 10 disintegrations per minute Rutherford (rd) – amount of radioactive substance which gives 10 6 disintegrations per second.

Rutherford and Soddy surmised four families of radioactive elements

Now A = A o - 4 where A o = original nuclide N  = # of  particles emitted N  = # of  particles emitted Z = Z o - 2 N  + N  These suggest there might exist 4 different series of radioactive elements, characterized by a different value m for the mass numbers of its members A = 4n + m

1 2 3 4 Series 4n Parent nucleus Th 232 Stable nucleus  Halflife ( T 1/2 , y) 1.39x10

6 4n + 1 4n + 2 4n + 3 Np 237  2.25x10

6 Ur  238 4.51x10

9 Ur  235 7.07x10

8 Series 1 – those with atomic weight being a multiple of 4 e.g. 228, 232, 236 Series 2 – those with atomic weight 4n + 1 e.g. 229, 233, 237 Series 3 – those with atomic weight 4n + 2 e.g. 230, 234, 238 Series 4 – those with atomic weight 4n + 3 e.g. 231, 235, 239

The shell model predicts that nuclei with proton numbers Z or neutron numbers N equal to 2 , 8 , 20 , 28 , 50 , 82 , and 126 are stable. e.g. lead Half-life -measures the life history of radioactive elements by counting the remaining element at a given time -the characteristic decay of a radioactive element is exponential -the time for a quantity of radioactive element to be reduced by half is # called half-life time time half-life

Halflife governs the rate of disappearance after it is isolated from the other members of the family T 1/2 = 0.693/   = disintegration constant; the fraction of atoms present that decay per unit time N = N o e  t

 -decay and neutrinos This is a result of the transformation of a neutron into a proton.

o n 1  p + e +  The energy spectrum is continuous.

Heines and Cowan verified the existence of neutrinos using the reaction P +   n + e -

FISSION

Enrico Fermi and Emilio Segre

, in 1934 bombarded uranium with neutrons and found several  -ray activities with different half-lives

Otto Hahn and Fritz Strassman

, in 1938 showed that One of the radioactive elements in the Fermi/Segre Experiment was an isotope of barium ( 56 Ba 141 ) Otto Frisch and Lisa Meitner suggested that uranium was Undergoing a nuclear fission process : U 235 + n U 236 X + Y + neutrons

n is a slow neutron U 236 is a highly unstable isotope X and Y are fission fragments X and Y can be either Ba 144 and Kr 89 or Xe 140 and Sr 94 Xe decays into Cs, then Ba to La and to Ce Sr decays into Y and then Zr The process releases neutrons and heat energy. The heavy nucleus captures a slow neutron. The Coulomb repulsion distorts the nucleus within 10exp-13 seconds. The nucleus fragments with the release of prompt neutrons. This may take only seconds or years delaying the release of neutrons.

Energy released in nuclear fission Before fission(isotopic mass) After fission (isotopic mass) U(235) = 235.0439 amu Ce(140) = 139.9054 amu n = 1.0087 amu Zr (94) = 93.9036 amu 236.0526 amu 2n = 2.0173 amu 6  = 0.0330 amu 235.8296 amu Mass difference = 0.233 amux931 MeV/amu = 208 MeV cf. with  -particle disintegration giving energy = 5 MeV and chemical combustion process energy of 4 eV.

Fast Breeder

– relies on fast, highly energetic neutrons

Fast Breeder

– relies on fast, highly energetic neutrons n

U 238 U 239  Np 239  Pu 239

n fp fp n

Disintegration of fertile isotope by fast neutron. The fission process releases heat energy as by-product.

Definitions of terms and equivalences Units of Energy: 1 joule (J) = 1 newton-meter 1 J = 0.738 ft-lb = 10 7 ergs 1 cal = 4.186 J 1 Btu = 252 cal = 1054 J 1 kWh = 3.6 x 10exp6 J 1 barrel of oil (BOE) = 5.8x10

6 Btu 1 Q = 10 18 Btu = 10 21 = 1.85x10

11 BOE = 3x10 14 kWh J

ENERGY RESOURCES A. Operating Reserves (in Q) Coal Oil Natural gas Shale TOTAL FOSSIL Hydroelectric (p.a.) Geothermal (natural) Fission (thermal) 27.1

1.7

1.9

0.87

32.0

0.1

0.002

2.0

B. Potential Reserves (in Q) Fission (fast breeder) Solar (p.a.) Geothermal (hot rock) Fusion (D-T) (lithium10 7 tons) (D-D) 1x10 3x10 10 6 200 1000 1000 ENERGY CONSUMPTION Current consumption = 12 terawatts (85% from fossil fuels); 1TW=5BBOE Projected for 9 B population = 27 TW for 14 B population = 42 TW

ICRP limits of radiation for individuals Organ or tissue Annual dose limits Gonads, red bone marrow Skin, bone, thyroid Hands & forearms, feet/ankles Other single organs Whole body (uniform) (in rem *) 0.5

3.0

7.5

1.5

0.5

* rem (roentgen-equivalent man) measures the dose equivalent in terms of the absorbed dose in rads = 100 ergs/gram, of energy deposition x quality factor e.g quality factor of X-rays =1; fast neutrons = 10 and Alpha particle radiation = 10

Some qualitative information 1. Existence of radioactive elements imply the Earth has not been around for an infinite period of time; the absence of actinium series imply the Earth is many times 2x10exp6 years. It is believed this series was initially created with the other three series.

2. Abundance of U235 and U238 (about 1:140) suggest that elements are perhaps not much older than 5x10exp9 years when the relative abundance of these were equal 3. Estimate of the age of meteorite is 4.5x10exp9 years, lower limit to the age of the universe itself, supporting the hypothesis of cataclysmic event that formed the elements

Some scientific processes 1. C 14 and H 3 are formed at about 10-15 km altitude in the presence of atmospheric O; the oxidation occurs to create 14 CO 2 and 3 HOH mixing with natural CO 2 and water in the atmosphere.

2. Assimilation of CO 2 14 CO 2 by plant life along with ordinary is subsequently transferred to animal life. The C 14 radioactive substance formed by cosmic rays become part of the reservoir of carbon that participate in the life cycles of living things making all living tissue somewhat with a degree of radioactivity which disintegrates at 15.5/minute/ gram of carbon. When the living thing dies, part of the carbon it contains may remain “out of circulation” for many years. This carbon does not mix with freshly formed radiation and decays as C 14 naturally.

3. 3 H dating used in problems connected with rainfall and meteorology, such as relation between ground water present at a given locality and local rainfall.

4. 7 Be used in the study of atmospheric mixing with its 53-day halflife

FUSION Hans Bethe suggested in 1938 that a nuclear reaction in which two nuclei came together to form a single heavier species plus the release of large quantities of energy.

Carbon cycle : 1 H + 12 C 7 N +  7 N 6 C + e + 

Some Fusion Reactions Threshold Plasma Average energy gain temperature per fusion* D + T He(4) + n 10 keV 1800 70 D + D T + p He(3) + n 50 keV D + He(3) He(4) + p T + He(3) He(4) + 2n + E 100 keV 180 1 eV = 11,600 K * ratio of energy released to energy absorbed per reaction

Experimental Requirements for Fusion 1. reaction rate must be high to produce useable quantities of power 2. power by fusion reaction must be greater by an order of magnitude than the power required to support the reaction P fus  3nT/  E P fus = n D n T   V  r (DT) E DT 3nT = thermal energy content of plasma  E = characteristic time in which plasma loses its energy due to all possible mechanisms such as conduction, convection, radiation n D n T = densities of deuterium and tritium components n = n D + n T = total density

E DT = total energy released per DT fusion reaction   V  r (DT) = total cross section for reactions P fus is maximum when n D = n T = n/2 Lawson criterion n  E  [12T/E DT ] /   V  r (DT) If T = 10 keV, E DT = 40 MeV;   V  r (DT) = 10 -23 m 3 /s n  E  1.5 x 10 20 s/m 3 (

minimum for DT reaction)

n  E T  10 21 keV s/m 3 (

triple product

)

Princeton TFTR

Courtesy Princeton Univ.

Main Parameters Total Fusion Power 1.5 Gw Burn Time 1000 s Plasma Current 21 MA Maximum Toroidal Magnetic Field 5.7 T Courtesy ITER Program