Nuclides 1

Introduction to Nuclidesthe big bang

The big bang theory www.uwaterloo.ca/~cchieh/cact/nuctek/universe.html

Einstein-Wheeler: "Matter tells space how to curve, and space tells matter how to move."1927 Lemaitre: The universe began with an explosion based on red shift. Hubble observed the red shift proportional to distance of stars from us. 1964 Penzias and Wilson discovered the cosmic microwave background (CMB) radiation, as due to remnants of big bang.

Depending on the outcome of the observations, the big bang theories will be abandoned, revised or extended to accommodate additional observartions.

What is in the universe?How did the universe begin?Where did materials come from?Can material and energy really inter-convert into each other?

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Nuclides 3

The Big Bang ViewAll energy (and matter) in the universe concentrates in a region smaller than a marble 12 billions years ago.

It started to expand and cool to a billion K. Elementary particles roamed free in a sea of energy.

Further expansion caused a drop in temperature and confined quarks in neutrons and protons.

Galaxies began to form.

             

           Galaxy clusters

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Hubble’s Observation

One method for gauging distance is to observe the apparent brightness of a galaxy.

          

           The red shift shows that the universe is constantly expanding

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Cosmologic Matters

Radiation: massless or nearly massless, photons (light) and neutrinos.

Baryonic matter (Nuclides): composed primarily of protons, neutrons and electrons; has essentially no pressure of cosmological importance.

Dark matter: exotic non-baryonic matter that interacts only weakly with ordinary matter; This form of matter also has no cosmologically significant pressure.

Dark energy: a bizarre form of matter, or perhaps a property of the vacuum itself; characterized by a large, negative pressure; a form of matter that can cause the expansion of the universe to accelerate

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What is the history of the universe?

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Nuclides composite particles of nucleons

Protons and neutrons are bound together into nuclei. Atoms contain a complement of electrons.

A nuclide is a type of atoms whose nuclei have a specific numbers of protons and neutrons.

Nucleons (protons and neutrons) are convenient units to consider nuclear changes, although the standard model considers quarks as basic components.

Like particles, nuclides are energy states, with amounts properties.

Some basic principles are seen for stability of nuclide.

A nuclideAEZ

A-mass numberZ-atomic number eg.

238U92

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Stable Nuclides

Stable nuclides remain the same for an indefinite period.

Some characteristics of stable nuclides:

Atomic number Z 83, but no stable isotopes for Z = 43 and 61.

There are 81 elements with 280 stable nuclides.

Usually there are more neutrons than protons in the nuclei.

Nuclides with magic number of protons or neutrons are very stable.

Pairing of nucleons (spin coupling) contributes to nuclide stability.

Is abundance of a nuclide related to its stability?

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Stable Nuclides

number of neutrons and protons

Find

N / Z for

4He2 = 116O8 =40Ar18 = 91Zn40 = 144Nd60 = 186Re75 =

209Bi83 =

N = # of neutrons

Z = # of protons

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Stable Nuclides

N/Z of some light nuclides

Z14 Si Si Si13 Al12 Mg Mg Mg . 11 Na10 Ne Ne Ne 9 F . 8 <- magic # . . . O O O 7 N N 6 C C . . 5 B B 4 Be . . 3 Li Li 2 . He He . . 1 P D . 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ->N

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Stable Nuclides

N/Z of nuclides 40 Zr . . . . . . . . + . . . XXX X X

39 Y X38 Sr X XXX 37 Rb X X 36 Kr X X XX X 35 Br . . . . . + . . X X34 Se XXXX X X33 As X32 Ge X XXX X . 31 Ga X X30 Zn . . . + . X XXX X . 29 Cu X X28 Ni X XXX X . . 27 Co X26 Fe X XXX . . 25 Mn + X24 Cr X XXX . . 23 v XX22 Ti XXXXX . . . 21 Sc X 20 Ca X X 2 2 3 4 5 01234567890123456789012345678901

N / A ratio increases as A increases

More stable isotopes for even Z than odd Z

More stable isotones for even N than odd N

More stable isotopes and isotones for magic Z and N

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Stable Nuclides

natural occurring heavy nuclides

Natural Occurring Isotopes of Heavy Elements (abundance)

76 Os 184 (0.018), 186 (1.59), 187 (1.64), 188 (13.3), 189 (16.1), 190 (26.4), 192 (41.0)77 Ir 191 (38.5), 193 (61.5)78 Pt 190 (0.0127), 192 (0.78), 194 (32.9), 195 (33.8), 196 (25.2), 198 (7.19)79 Au 197 (100)80 Hg 196 (0.146), 198 (10.02), 199 (16.84), 200(23.13), 201(13.22), 202(29.8), 204(6.85)81 Tl 203 (29.5), 205 (70.5)82 Pb 204 (1.4), 206 (25.1), 207 (21.7), 208 (52.3)83 Bi 209 (100)

90 Th 232 (100% half life 1.4x1010 y)

92 U 235 (0.720, half life 7.04x108 y), 238 (99.276, half life 4.5x109 y)

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Stable Nuclides

pairing of nucleons

Effect of Paring Nucleons

Z N # of stable stable nuclides

even even 166even odd 57odd even 53odd odd *4

total 280

*They are: 2D1, 6Li3, 10B5, & 14N7

Two protons or neutrons occupy a quantum state, due to their ½ spin.

Pairing nucleons stabilises nuclides, leading to a large number of stable nuclides with even Z and N.

No stable isotopes for Z = 43 or 61.

No stable isotones with N = 19, 31, 35, 39, 61, 89

More stable isotopes for even Z than odd Z and for even N than odd N

Elements with even Z are more abundant than those with odd Z of comparable mass.

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Stable Nuclides

magic numbers of nucleons

Magic numbers are 2, 8, 20, 28, 50, 82, and 126.

Double-magic number nuclides: 4He2, 16O8, 40Ca20, 48Ca20, & 208Pb82.

4He2 as alpha particles, abundant in the universe, 16O8 abundant on Earth.

Six stable isotopes of Ca20, 5 stable isotopes of Ni28, high for their masses.

Large number of stable isotopes and isotones with Z & N = 50 and 82.

The heavies stable nuclide 209Bi83 has 126 neutrons.

O8, Ca20, Ni28, Sn50 and Pb82 have relative high abundance.

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Stable Nuclides

abundances of elementsAtomic Abundance (AA) of Elements of the Inner Solar System Excluding the Sun

Log (AA)

0 O. . . MgSi . Fe .-1 Ni. . . Al S Ca .-2 Na. . C . P . Ti CrMCo . . . . .-3 Cl V Cu SeAs. . . . . . . . . .-4 N F Sn Pb. . Be . . . Sc Zr . . . W .-5 LiB Mn Ba. . . .Sc . Y. . . . Pt.-6 Ga Ru Sb CeNdSm Os. . . . . . PdCd. . Dy YbHf IrAu-8 Br Pr. . . . . . RhAgIn I La . EuTbHoTu Lu .Tl-9. . . . . . Mo . . . Re .-10

0 1 2 3 4 5 6 7 8 Mass No. 12345678901234567890123456789012345678901234567890123456789012345678901234567890

Even Z elements are more abundant than odd Z ones of comparable mass.

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Stable and Radioactive Nuclidesmass and stability of nuclides

Mass and energy are equivalent, E = m c2.

Relative mass is the key for stability of nuclides.

Energy drives changes.

If a system can lower its energy, it will.

Unstable nuclides undergo decay or fission, releasing energy stabilises the system.

Discuss the stability of carbon isotopes.

Half life9C 127. ms10C 19.3 s11C 20.3 m12C stable13C stable14C 5730. y15C 2.45 s16C 0.75 s

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Stable and Radioactive Nuclides

binding energy

The binding energy (BE) of a nuclide is the energy released when the atom is synthesized from the appropriate numbers of hydrogen atoms and neutrons.

Z H + N n = AEZ + BE

or Z mH + N mn = mE + BEwhere mH, mn, and mE are masses of H, n, and AEZ respectively.Eg

BE = Z mH + N mn - mE

BE (3He) = (2*1.007825 + 1.008665 - 3.01603) 931.481 MeV = 7.72 MeV

BE (4He) = (2*1.007825 + 2*1.008665 - 4.00260) 931.481 MeV = 28.30 MeV

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Stable and Radioactive Nuclides

average binding energyThe binding energy and averagebinding energy of some nuclides

Nuclide BE BE / A MeV MeV / nucleon

3He2 7.72 2.574He2 28.3 7.0816O8 127.6 7.9856Fe26 492.3 8.79 54Fe26 471.76 8.74 208Pb82 1636.44 7.87 238U92 1801.7 7.57

Variation of the Average Binding Energyas a Function of Mass Number A

Fe

U

3He

BEa

v

A

BE A

A

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The Average Binding Energy Curve

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Stable and Radioactive Nuclides

mass excess (ME)

The difference between the mass of a nuclide and its mass number, A, is the mass excess (ME),

ME = mass - A.

Masses (amu) of some entitiesH 1.00782503 18O 17.999162D 2.014102 54Fe 54.938296 3H 3.016049 56Fe 55.9349394He 4.002603 206Pb 205.97587212C 12.000000 209Bi 208.980414C 14.003242 235U 235.04392416O 15.994915 238U 238.055040 What are the MEs for the

nuclides listed here?

Which is the standard?

Which have negative MEs?

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Stable and Radioactive Nuclides

mass excess (ME) and average -BE

Comparison of mass excess and average binding energy (amu)

Nuclide Mass ME -BE average BE

H 1.007825 0.007825 0 0n 1.008665 0.008665 0 0

3He 3.01603 0.01603 -0.00276 0.008284He 4.00260 0.00260 -0.0076 0.030412C 12.000000 0 -0.00825 0.0989416O 15.994915 -0.005085 -0.00857 0.1369

40Ca 39.96259 -0.03741 -0.00917 0.3669 54Fe 53.939612 -0.060388 -0.00938 0.506556Fe 55.934939 -0.065061 -0.00944 0.52851

208Pb82 207.976627 -0.023373 -0.00845 1.757238U92 238.050784 0.050784 -0.00813 1.934

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Stable and Radioactive Nuclides

fission and fusion energy and ME

Variation of ME with Afor Some Stable Nuclides

ME amu

0.01

0.005

0.0

–0.005

A

H

3He

4He12C

FePb

U

n

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Stable and Radioactive Nuclides

application of mass excess (ME)

Like masses, the ME can be used to calculate energy of decay, because the same scale is used for both.

eg:

ME’s of 40Sc21 and 40Ca20 are -20.527 and -34.847 MeV respectively. Estimate the energy of decay for

40Sc21 40Ca20 + + or 40Sc21 + e– 40Ca20

solution:Edecay = -20.527 - (-34.847) = 14.32 MeV

Edecay includes 1.02 MeV for the positron-electron pair for + decay.

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Stable and Radioactive Nuclides

ME of isobars

In49 Sn50 Sb51 Te52 I-53 Xe54 Cs55 Ba56

-0.0896 -0.0943 -0.0958 -0.0967 -0.0944 -0.0915 -0.0870 -0.0808

Mass Excesses of Isobarswith Mass number 123

-0.08 amu

-0.09

-0.10 In Sn Sb Te I Xe Cs Ba49 50 51 52 53 54 55 56

–

+, EC

Mass excesses (amu) of isobars with mass number 123:

Z

ME

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Stable and Radioactive Nuclides

BE of isobars Isobars with MassNumber 57

-494 – Cr-495

-496 _ Ni-497

-498 – – Mn Co-499

-500 – 24 25 Fe 27 28

–

+

EC

Plots of BE an ME are very similar, and either one can be used to show the decay of isobars.

Only 57Fe26 is stable for isobars of mass 57

.Mass .BE

.amu .amu

Cr24 56.9434 0.53031 Mn25 56.9383 0.53462 Fe26 56.9354 0.53667

Co27 56.9363 0.53493

Ni28 56.3980 0.53240

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Stable and Radioactive Nuclides

problem types

Evaluate the BE of a nuclide

tell nuclide with zero BE

evaluate ME of a nuclide

tell nuclide with zero ME

evaluate decay energy

estimate decay mode

predict the stable isobar(s)

estimate max kinetic energy of beta or positrons in beta decay

Mass and BE of mass 57 isobars

.Mass .BE

.amu .amu

Cr24 56.9434 0.53031 Mn25 56.9383 0.53462 Fe26 56.9354 0.53667

Co27 56.9363 0.53493

Ni28 56.3980 0.53240

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Stable and Radioactive Nuclides

ME of isobarscontinue

Relative Mass Differences (MeV) forIsobars with Mass Number 120.

Ba22

20

18 Cs16 Ag14

12

10 Xe 8 Cd I 6 In 4

2 Sb Te 0 Sn 47 48 49 50 51 52 53 54 55 56

Pairing of nucleons plays a role for stability of isobars with even mass numbers.

There are even-even and odd-odd type of nuclides in isobars of even mass numbers

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Stable and Radioactive Nuclides

a semi-empirical equation for BE

BE(A,Z) = 14.1A - 13A2/3 - - + Ea

3/1

26.0

A

ZA

ZA 2)2(20

Proportional to A

Decrease due to surface tension

Instability due to p

Instability due to neutron to proton ratio

Pairing of nucleon

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Nuclidessummary

The big bang

Factors for stable nuclides

mass and stability

Variation of ME with Afor Some Stable Nuclides

ME amu

0.01

0.005

0.0

–0.005

A

H

3He

4He12C

FePb

U

n

Relative Mass Differences (MeV) forIsobars with Mass Number 120.

Ba22

20

18 Cs16 Ag14

12

10 Xe 8 Cd I 6 In 4

2 Sb Te 0 Sn 47 48 49 50 51 52 53 54 55 56