Probing the Subatomic World

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

The nucleus: AMZ , e.g. 14C6

Z = atomic number, # of protons/electronsA = atomic mass, total # of nucleons N = A – Z = number of neutrons

ISOTOPES – nuclides with identical Z ISOBARS – 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 oneis the neutron (proton) number of the other

Which are isotopes, isobars, isotones, mirror nuclei?

12B5, 14C6,14N7, 14O8, 16O8

Isotopes - 14O8, 16O8

Isobars - 14C6,14N7, 14O8

Isotones - 12B5, 14N7

Isomers - 14O8, 16O8

Mirror nuclei - 14C6, 14O8

NUCLEAR SIZE (R. Hofstadter) –mean electromagnetic radius, i.e. the radius to the 50% point in the

density distribution

Re = (1.07 0.02) A1/3 x 10-15 m = 1.07 A1/3 F

1 F (fermi) = 10-15 m

What is the mass number of a nucleus having a radius one third that of 27Al13?

Discovery of radioactivity Becquerel – uranium

M. Curie – polonium and radium Debierne and Giesel – actinium

O. Hahn – radiothorium, mesothorium•Radioactive emissions

o alpha particles – helium nucleuso 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) + 2He4 

- 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 , , ?

 

source

x – B-fieldx

Geiger counter- measures radioactivity

Units:

Curie (Cu) – quantity of any radioactive material giving 3.7 x 1010 disintegrations per minute

Rutherford (rd) – amount of radioactive substance which gives 106 disintegrations per second.

Rutherford and Soddy surmised four families of radioactive elements

Now A = Ao - 4

where Ao = original nuclide

N = # of particles emitted

N = # of particles emitted

Z = Zo - 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

Series 4n 4n + 1 4n + 2 4n + 3Parent nucleus Th232 Np237 Ur238 Ur235

Stable nucleus Halflife ( T1/2, y) 1.39x106 2.25x106 4.51x109 7.07x108

1 2 3 4

Series 1 – those with atomic weight being a multiple of 4 e.g. 228, 232, 236Series 2 – those with atomic weight 4n + 1 e.g. 229, 233, 237Series 3 – those with atomic weight 4n + 2 e.g. 230, 234, 238Series 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 126are 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

#

timehalf-life

Halflife governs the rate of disappearance after it isisolated from the other members of the family

 T1/2 = 0.693/

  = disintegration constant; the fraction of atoms

present that decay per unit time 

N = No e- t

-decay and neutrinos 

This is a result of the transformation of a neutron into a proton.

on1 p + e- +

 The energy spectrum is continuous. 

Heines and Cowan verified the existence of neutrinos using the reaction

 P + n + e-

 

FISSIONEnrico Fermi and Emilio Segre, in 1934 bombarded uranium with neutrons and found several -rayactivities with different half-lives

Otto Hahn and Fritz Strassman, in 1938 showed thatOne of the radioactive elements in the Fermi/SegreExperiment was an isotope of barium (56Ba141)

Otto Frisch and Lisa Meitner suggested that uranium wasUndergoing a nuclear fission process:

U235 + n U236 X + Y + neutrons

n is a slow neutronU236 is a highly unstable isotopeX and Y are fission fragments

X and Y can be either Ba144 and Kr89 or Xe140 and Sr94

Xe decays into Cs, then Ba to La and to CeSr decays into Y and then Zr

The process releases neutrons and heat energy. The heavynucleus captures a slow neutron. The Coulomb repulsion distorts the nucleus within 10exp-13 seconds. The nucleusfragments with the release of prompt neutrons. This may takeonly 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 amun = 1.0087 amu Zr (94) = 93.9036 amu 236.0526 amu 2n = 2.0173 amu 6- = 0.0330 amu

235.8296 amuMass difference = 0.233 amux931 MeV/amu = 208 MeVcf. 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

fp

fp

n

nU238 U239

-

Np239

Pu239

-

n

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

Definitions of terms and equivalencesUnits of Energy: 1 joule (J) = 1 newton-meter 1 J = 0.738 ft-lb = 107 ergs 1 cal = 4.186 J

1 Btu = 252 cal = 1054 J1 kWh = 3.6 x 10exp6 J1 barrel of oil (BOE) = 5.8x106 Btu1 Q = 1018 Btu = 1021 J = 1.85x1011 BOE = 3x1014 kWh

ENERGY RESOURCESA. Operating Reserves (in Q)

Coal 27.1Oil 1.7Natural gas 1.9

Shale 0.87TOTAL FOSSIL 32.0

Hydroelectric (p.a.) 0.1Geothermal (natural) 0.002Fission (thermal) 2.0

B. Potential Reserves (in Q)Fission (fast breeder) 200Solar (p.a.) 1000Geothermal (hot rock) 1000Fusion (D-T) 1x106

(lithium107 tons) (D-D) 3x1010

ENERGY CONSUMPTIONCurrent consumption = 12 terawatts (85% from fossil fuels); 1TW=5BBOEProjected for 9 B population = 27 TW for 14 B population = 42 TW

ICRP limits of radiation for individuals

Organ or tissue Annual dose limits(in rem*)

Gonads, red bone marrow 0.5Skin, bone, thyroid 3.0Hands & forearms, feet/ankles 7.5Other single organs 1.5Whole body (uniform) 0.5

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

Some qualitative information1. 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 processes1. C14 and H3 are formed at about 10-15 km altitude in the presence of atmospheric O; the oxidation occurs to create 14CO2 and 3HOH mixing with natural CO2 and water in the atmosphere.2. Assimilation of 14 CO2 by plant life along with ordinary CO2 is subsequently transferred to animal life. The C14

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 C14 naturally.

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

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

FUSION

Hans Bethe suggested in 1938 that a nuclear reactionin which two nuclei came together to form a singleheavier species plus the release of large quantities ofenergy. Carbon cycle : 1H + 12C 7N + 7N 6C + e +

Some Fusion ReactionsThreshold Plasma Average energy gain temperature per fusion*

D + T He(4) + n 10 keV 1800

D + D T + p 50 keV 70

He(3) + n

D + He(3) He(4) + p 100 keV 180

T + He(3) He(4) + 2n + E

1 eV = 11,600 K* ratio of energy released to energy absorbed per reaction

Experimental Requirements for Fusion1. 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  Pfus 3nT/E

  Pfus = nDnT Vr (DT) EDT

  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

nDnT = densities of deuterium and tritium components

 n = nD + nT = total density

EDT = total energy released per DT fusion reaction

  Vr (DT) = total cross section for reactions

 Pfus is maximum when nD = nT = n/2

 Lawson criterion nE [12T/EDT] / Vr (DT)

 

If T = 10 keV, EDT = 40 MeV; Vr (DT) = 10-23 m3/s

  nE 1.5 x 1020 s/m3 (minimum for DT reaction) 

  nE T 1021 keV s/m3 (triple product)

Courtesy Princeton Univ.

Princeton TFTR

Courtesy ITER Program

Main Parameters

Total Fusion Power 1.5 GwBurn Time 1000 sPlasma Current 21 MAMaximum Toroidal Magnetic Field 5.7 T