Structure of atomic nucleus

2006/07

Structure of atomic nucleus (Bohr-Sommerfeld model, 1915)

The created models are based on the recent knowledge of the science.

Atom models according to Democritos, Dalton, Thomson, Rutherford, Bohr

Frank-Hertz experiment, photoelectric effect, Compton scattering, Zeeman-effect, Stern-Gerlach experiment,

Pauli, de Broglie, Einstein, Schrödinger, Wiegner, Teller, Szilárd, Yukawa, Sommerfeld ...

Elements of the atom:

Electron cloud (electrons, e-) and nucleus (nucleons: protons + neutrons, p+, n0)

Categorisation of atomsContent

(number of protons: Z, number of neutrons: N, num. of nucleons: N+Z=A)

isotope: same Z, different N ( 11H és 2

1H)nuclid: same content (N, Z equals in each: one type of isotop)isoton: same N, different Z ( 2

1H, 32He )

isobar: same A, different N (86C, 8

5B ) isomer: same content, different energystates

Stabilitystable nuclei

Radioactivity not occurs. Approx. 264 nuclei, 12C, 14N, 16O natural radionuclids

Natural radionuclids can be found in the Universe from the time of Big-Bang. These have long half-life time. 26 nuclei.238U ( T = 4,47·109 year), 40K ( T = 1,28·109 year), 87Rb ( T = 48·109 year)

artificial radionuclids Made by people (scientist). Approx. 2000, 60Co, 137Cs, 24Na

Categorisation of particles, classification

fermions: ½ spin particles –

Fermi-Dirac statistic

bosons: integer spin number –

Bose-Einstein statistic

An electron can be classified as: fermion, lepton

A proton (neutron): fermion, baryon

InteractionCurrent

TheoryMediator

Rel. strength

range(m)

Long-Distance Behavior

Strong

Quantum chromo-dynamics

(QCD)

gluons 1038 10-15

Electro-magnetic

Quantum electro-

dynamics(QED)

photons 1036 ∞   

Weak

Quantum flavour-

dynamics(GWS theory)

W and Z bosons

1025 10-18           

GravityGeneral Relativity gravitons 1 ∞   

Interactions

Rutherford’s nucleus alteration experiment (1917)

Irradiated nitrogen gas with α-particles:

Internuclear reactions took place, therefore it is not compulsory that the alteration of elements is allways connected to radioactive decomposition.

HOHeN 11

178

42

147

Ernest Rutherford

1871-1937

Discovery of the neutron

Experiment of Bothe and Becker (1930)

They bombed Berilium with α-particles, and detected a ray with great penetration ability, which did not diverge in magnetic nor in electric field. Neutral.

Walther Bothe

1891-1957

(Nobel-prize in physics,1954)

Chadwick’s interpretation (1932)

During the collision of Be and α-particle an unknown particle radiation was found, which had the same mass as a proton but had not any electric charge.

He named this new particule as neutron.

nCHeBe 10

126

42

94 James Chadwick

1891-1974

(Nobel-prize in physics 1935)

Heisenberg and Tamm (1932)

They developed a new nucleus model including neutrons, too.

New signification is brought to atomic number!

High energy -particles can cause in certain ”light chemical elements” (Be, B, Li), that a special radiation with high penetration ability leaves the irradiated matter. It was thought to be X-ray.

He assumed that a neutral particle with approximately same mass as proton is emitted.

PropertiesThe free neutron is not stable, its mean half-life time is 885 s= 18,6 min.Its decomposition is caused by the weak interaction.A lot of nuclei can absorb neutron radiation → absorption → generally radioactive isotopes appear!

Neutron (quarkstructure) 1932, James Chadwick

epn0 Atom energy!

Discovery of the positron positively charged electron (antiparticle)

Iréne Curie and Fréderic Joliot-Curie

Aluminium foil irradiated by α-particles:

The arisen phosphor isotope does not occurs in the nature, immediately transforms to stable silicium.

How did one positive charge disappear?

During the process one proton transformed to neutron!

+ radiation:

nPHeAl 10

3015

42

2713

SiP 3014

3015

� enp 0

http://en.wikipedia.org/wiki/

Scattering of -particles on nuclei.Composed of two u and one d quark, the proton is a baryon (its spin is ½ → fermion).The main properties of the proton are determined by those three (two type) quarks.The quarks are bound together by the strong interaction.The proton’s mass is much larger then the total mass of the included quarks. Maybe it contains more particles?The values of spin-quantumnumber and magnetic moment is exactly the sum of the appropriate values (respectively) of the quarks.

The proton (quarkstructure)1918, Ernest Rutherford

Charge: q = +1,6 10⋅ -19 C

Resting mass: 1,67 10⋅ -27 kg =1836,15 × me

Magnetic momentum

1,41 10⋅ -26 J T-1

Spin 1/2 → fermion

quarkstructure uud → baryon (neutrally coloured)

Properties of the proton

Deficit of mass – binding energy

(Specific) binding energy ~ A! each nucleon(independently of already involved ones) is bound with approx. 7-8 MeV to the nucleus.

• The mass of composite nuclei is always less than the total mass of its components (protons and neutrons).• The virtually missing mass value is proportional to the binding energy.• Energy is disengaged (released), while a nucleus is constructed from free nucleons.

2cmE

nucnpr mNmZmm

mass-energy equivalency of Einstein

Quarksname sign mass

m0 (GeV/c2)electr. charge

(*e)

Up u 0,0015-0,005  2/3

Down d 0,017-0,025 -1/3

Charm c 1,1-1,4  2/3

Strange s 0,06-0,17 -1/3

Top / True t 165-180  2/3

Bottom / Beauty b 4,1-4,4 -1/3

Colours of quarksThis colour is not a real colour (not connected with eye perception!) but the properties are based on the analogy of the real colours.Quarks does not exist separately (free). All of the quarks can have all of the three colours. red, green and blue (r, g, and b).Quarks generally occur in neutral-colour combinations.The strong interaction affects every colour-charged particles: for example the baryons.Quarks participate in all four interactions!

Nuclear force – strong interactionProtons push aside one another because of the Coulomb-force of identical charges, however the nucleus is stable. There must be a short-distanced but strong interaction to compensate the repulsion of electric charges.

The strong interaction appears amongst nucleons (neutrons too!).In quantum-theory the strong interaction is explained by the quantum-chromodynamics (QCD) theory. The mediators of the interaction are the gluon particles, and affects the colour-charged particles: quarks, gluons and other more complex particles composed of the previously mentionned ones: baryons and mesons, (nucleons are also baryons.)

▪ high intensity (strong) ▪ short distance (10-15m)

▪ electric charge independent ▪ attracting effect

▪ p-p, p-n, n-n interactions have the same magnitude

The weak interaction

Radioactive -decomposition (decay of proton and neutron).

HistoryPauli supposed that meanwhile of b-decomposition one neutral particle of approximately zero mass (called neutrino) carries a part of the energy away, and it is indetectable. In 1934, Enrico Fermi generated his theory which affirmed this presumption (four-fermion interaction).

Affects all of the leptons and quarks. The neutrino (and antineutrino) participates only in this type of interaction.Mediators are W- és Z-bosons. W+, W- are electrically charged, Z0 is neutral boson.

Neutron decomposition can be interpreted as the following:

first, neutron emits one W-boson and that inmediately decompose to electron and antineutrino. Meanwhile the neutron transforms to proton. (d → u transformation)

Model’s of the nucleus

Atomic shell model(sphere symmetric)

The atomic shell model is based on the microscopic properties (energy levels) of the atom.Quantummechanics can interpret the behavior of the electrons in the electronshell. Certain properties of the nucleus show periodic behavior. Is it capable to describe the behavior of the neutron too?

Nucleus with magic numbers:We can get a stabil nucleus if either of the number of the nucleon (N, Z) assumes the value of 2, 8, 20, 50, 82, 126.

Bartlet, Elsasser, 1934: „independent particule model”Jensen and Göppert-Mayer, 1949: atomic shell model

All of the nucleon create a collective potentialfield, wherein nucleons can move independently from each other.The nucleons Schrödinger equation’s with quantified parameters ( energy, angular momentum, magnetic momentum, spin) characterize the atomic shells. (spin can only have the value of ½, Pauli-principle is valid)Atoms with enclosed atomic shells are more stable!

Analogy with electron shells! Several experimental results are not confirmed with this model!

Atomic shell model(sphere symmetric)

Bohr showed it first that some properties of atoms (nucleus) resembles to a liquid drop’s properties (especially in the case of heavy atoms)Observations:1. Each of the nucleons is bound with (almost) the same energy.2. This concludes that the total binding energy of the nucleus is proportional to the number of nucleons (A). 3. The volume of the nucleus is proportional to the number of nucleons (A). Hofstaedter4. This concludes that the density of nucleus is the same in the case of every atom.

Liquid drop model

Carl von Weizsäcker( macroscopic properties) Explains a lot of phenomena (binding energy, mass, stability of nuclei).Based on the property-similarity of atoms and liquid drops: spherical form, size-independency of density, the components interact only with their proximate neighbours.

r: radius of nucleus (constant, independ. of atom type)A: atomic number

Liquid drop model

30 Arr

mr 150 102

3

2

2

3

1

23

22

AA

AZ

A

ZAAk

According to the liquid drop model the binding energy is formed from different energies.

Terms explained by classical physics:Nucleons move (exist) in the potencial field of the neighbouring nucleons:

volume energyThe nucleons on the surface (outer side) have less „neighbours” surface energyElectrostatic energy is also present because of charged protons Coulomb-energy

A

3

2

A

3

1

2

A

Z

3

2

2

3

1

23

22

AA

AZ

A

ZAAk

Other terms explained by quantum theory:

Pauli (asymmetry) energy (fermions, Pauli-law)

anti-Hund (pairing) energy

|| , if the number of protons and neutrons both are even (2H,6Li,10B,14N)

= 0 , if the one of the numbers of protons and neutrons is even, the other odd (2H,6Li,10B,14N)

-|| , if the number of protons and neutrons both are odd, frequent in nature

A

AZ

2

2

3

2

A

Parameters are experimentally determined – semiempiric formule!

The fit is good, except for the light atoms and the atoms connected to the magic numbers.Reason: These atoms contain closed atomic shells and that phenomena is not taken into account in the liquid drop model!

Maximum: between 55-60!

One nucleons’ binding energy as the function of atomic number

The ratio of surface and volume energies change!

(r2/r3 = 1/r)

Effect of Coulomb force increases!

Unified modelSome of the experiments showed that the shape of atoms can deviate from a spherical symmetry (becomes elliptical).According to L.J. Rainwater (1950) a nucleon(group) out of the last closed shell can „polarise” and distort the nucleus, causing some deformation.The deformed nucleus can undergo some collective motion:rotation, vibration (that motion can appear in the sphere form too).S.G. Nilsson, Aage Bohr, B.R. Mottelson improved the shell model (1955-1968). According to the unified model the total momentum of the nucleus can not be calculated normal way (j=l+s), rather taking into account the new momentum (R) originating from the rotation of the distorted nucleus. Therefore: J=j+R.

Atomic reactions of elements: -decomposition, fusion, fission

Atomic number less than 56:

Atomic number bigger than 56:

Ba13556

epn0

� enp 0

Enrico Fermi

1901-1954

Nobel-price in1938

and fusion

and fission

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