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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?

Nuclides

The Big Bang View

All 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

Nuclides

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

Nuclides

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

Nuclides

Nuclides composite particles of nucleons

A nuclideAEZA-mass numberZ-atomic number eg.238U92

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.

Nuclides

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?

Nuclides

Stable Nuclidesnumber of neutrons and protons

Z = # of protons

Find

N / Z for

4He2 = 116O8 =40Ar18 = 91Zn40 = 144Nd60 = 186Re75 =209Bi83 =

N = # of neutrons

Nuclides

Stable NuclidesN/Z of some light nuclides

Z

14 Si Si Si

13 Al

12 Mg Mg Mg .

11 Na

10 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

Nuclides

Stable NuclidesN/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 X

33 As X

32 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

Nuclides

Stable Nuclidesnatural 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)

Nuclides

Stable Nuclidespairing of nucleons

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.

Effect of Paring Nucleons

Z N # of stable stable nuclides

even even 166

even odd 57

odd even 53

odd odd *4

total280

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

Nuclides

Stable Nuclidesmagic 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.

Nuclides

Stable Nuclidesabundances of elements

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

Nuclides

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 life

9C 127. ms

10C 19.3 s

11C 20.3 m

12C stable

13C stable

14C 5730. y

15C 2.45 s

16C 0.75 s

Nuclides

Stable and Radioactive Nuclidesbinding 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 ZmH + Nmn = mE + BEwhere mH, mn, and mE are masses of H, n, and AEZ respectively.Eg
- BE = ZmH + Nmn - 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

Nuclides

Stable and Radioactive Nuclidesaverage binding energy

The binding energy and averagebinding energy of some nuclides

Nuclide BEBE / 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

BE A

A

Nuclides

The Average Binding Energy Curve

Nuclides

Stable and Radioactive Nuclidesmass 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 entities

H 1.00782503 18O 17.99916

2D 2.014102 54Fe 54.938296

3H 3.016049 56Fe 55.934939

4He 4.002603 206Pb 205.975872

12C 12.000000 209Bi 208.9804

14C 14.003242 235U 235.043924

16O 15.994915 238U 238.055040

What are the MEs for the nuclides listed here?

Which is the standard?

Which have negative MEs?

Nuclides

Stable and Radioactive Nuclidesmass excess (ME) and average -BE

Comparison of mass excess and average binding energy (amu)

Nuclide MassME -BE average BE

H 1.007825 0.007825 0 0 n 1.008665 0.008665 0 03He 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 0.136940Ca 39.96259 -0.03741 -0.00917 0.3669 54Fe 53.939612 -0.060388 -0.00938 0.506556Fe 55.934939 -0.065061 -0.00944 0.52851208Pb82 207.976627 -0.023373 -0.00845 1.757238U92 238.050784 0.050784 -0.00813 1.934

Nuclides

Stable and Radioactive Nuclidesfission and fusion energy and ME

Nuclides

Stable and Radioactive Nuclidesapplication 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

40Sc2140Ca20 + b+ or 40Sc21 + e–40Ca20solution: Edecay = -20.527 - (-34.847) = 14.32 MeV

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

Nuclides

Stable and Radioactive NuclidesME of isobars

ME

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

Z

In49 Sn50Sb51 Te52 I-53 Xe54 Cs55 Ba56-0.0896 -0.0943 -0.0958 -0.0967 -0.0944 -0.0915 -0.0870 -0.0808

Nuclides

Stable and Radioactive NuclidesBE of isobars

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

Nuclides

Stable and Radioactive Nuclidesproblem 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

Nuclides

Stable and Radioactive NuclidesME of isobarscontinue

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

Nuclides

Stable and Radioactive Nuclidesa semi-empirical equation for BE

Instability due to p

Pairing of nucleon

Proportional to A

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

Instability due to neutron to proton ratio

Decrease due to surface tension

Nuclides

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