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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

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slide1

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/electrons

A = atomic mass, total # of nucleons

N = A – Z = number of neutrons

slide2

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 one

is the neutron (proton) number of the other

Which are isotopes, isobars, isotones, mirror nuclei?

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

slide3

Isotopes - 14O8, 16O8

Isobars - 14C6,14N7, 14O8

Isotones - 12B5, 14N7

Isomers - 14O8, 16O8

Mirror nuclei - 14C6, 14O8

slide4

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?

slide5

Discovery of radioactivity

  • Becquerel – uranium
  • M. Curie – polonium and radium
  • Debierne and Giesel – actinium
  • O. Hahn – radiothorium, mesothorium
  • Radioactive emissions
  • alpha particles – helium nucleus
  • beta particles – fast electrons
  • gamma rays – em radiation with wavelengths greater than
  • X-rays
slide6

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 , , ?
slide7

x – B-field

x

source

slide8

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

slide9

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

slide10

1 2 3 4

Series 4n 4n + 1 4n + 2 4n + 3

Parent nucleus Th232 Np237 Ur238 Ur235

Stable nucleus 

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

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

slide11

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

slide12

Halflife governs the rate of disappearance after it is

isolated 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

slide13

 -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-

slide14

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 (56Ba141)

Otto Frisch and Lisa Meitner suggested that uranium was

Undergoing a nuclear fission process:

U235 + n U236 X + Y + neutrons

slide15

n is a slow neutron

U236 is a highly unstable isotope

X 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 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.

slide16

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

slide17

Fast Breeder – relies on fast, highly energetic neutrons

fp

Pu239

-

n

-

fp

U238

U239

Np239

n

n

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

slide18

Definitions of terms and equivalences

Units 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 J

1 kWh = 3.6 x 10exp6 J

1 barrel of oil (BOE) = 5.8x106 Btu

1 Q = 1018 Btu = 1021 J

= 1.85x1011 BOE

= 3x1014 kWh

slide19

ENERGY RESOURCES

  • Operating Reserves (in Q)
  • Coal 27.1
  • Oil 1.7
  • Natural gas 1.9
  • Shale 0.87
  • TOTAL FOSSIL 32.0
  • Hydroelectric (p.a.) 0.1
  • Geothermal (natural) 0.002
  • Fission (thermal) 2.0
slide20

B. Potential Reserves (in Q)

Fission (fast breeder) 200

Solar (p.a.) 1000

Geothermal (hot rock) 1000

Fusion (D-T) 1x106

(lithium107 tons)

(D-D) 3x1010

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

slide21

ICRP limits of radiation for individuals

Organ or tissue Annual dose limits

(in rem*)

Gonads, red bone marrow 0.5

Skin, bone, thyroid 3.0

Hands & forearms, feet/ankles 7.5

Other single organs 1.5

Whole body (uniform) 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

slide22

Some qualitative information

  • 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.
  • 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
slide23

Some scientific processes

  • 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 CO2and waterin
  • 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.
slide24

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

slide25

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 : 1H + 12C 7N + 

7N 6C + e + 

slide26

Some Fusion Reactions

Threshold 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

slide27

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

Pfus 3nT/E

Pfus = nDnT Vr (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

slide28

EDT = total energy released per DT fusion reaction

Vr (DT) = total cross section for reactions

Pfus is maximum when nD = nT = n/2

Lawson criterion nE  [12T/EDT] /Vr (DT)

If T = 10 keV, EDT = 40 MeV; Vr (DT) = 10-23 m3/s

nE  1.5 x 1020 s/m3 (minimum for DT reaction)

nE T 1021 keV s/m3 (triple product)

slide29

Princeton TFTR

Courtesy Princeton Univ.

slide30

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