Atomphysics.The atomic nucleus. Radioactivity.

12. 10. 2010.Biophysics, Miklós Nyitrai

Why do we all believe that atomphysics is easy and joyful?

Philosophers / scientists

SchrödingerAristoteles Dalton BohrJ.J.Thompson

Fermi Einstein and SzilárdTeller Yukawa

Pauli

http://www.cartage.org.lb/en/themes/sciences/physics/Atomicphysics/Atomicstructure/AtomicTimeline/AtomicTimeline.htm

http://library.thinkquest.org/17940/texts/timeline/timeline.html

Pierre, Marie Curie

Previously discussed

• The structure of atoms• Quantum numbers• Dual nature of light

The concept of atom

Democritos,

Dalton,

Thomson,

Rutherford,

Bohr

Frank-Hertz experiment, photoelectric effects, Comptonscattering, Stern-Gerlach experiment.

The appearance of nucleus in the atom models

+_

_ +

++

+

”All matter is composed of atoms, which are bits of matter

too small to be seen. These atoms CANNOT be further

split into smaller portions.”

The word atom has the origin: atomos (ατομοσ), a Greek word meaning uncuttable (indivisible).

Democritus

Thompson’s atomic model (1906)

electrons• Discovery of the electron.• The plum-pudding model.• There is no nucleus mentioned. Thepositive charge is spread in a ”large” volume.

Atomic models based on experiments:

Atomic nucleus does not exist!

+_

_ +

++

+

+ +

++

+

Rutherford model (1911)

Discovery of the nucleus.Positively charged nucleus exists and theelectrons move in the substance.Neutron and proton are not mentioned!

R0 = 1.4 · 10-15 m

experimental setup

α-particles

Bohr-Sommerfeld model; 1915• The electron travels around the nucleus on a circular orbit.• The parameters of orbits are quantized: energy, angular momentum, radius

Bohr model (Hydrogen atom; 1913)

α

What does an atom consist of?According to Bohr’s model (1913):

• Negatively charged electrons → e- cloud• Positively charged nucleus → proton and neutron werenot known!• Spatial connection between the nucleus and electron: itcan not appear everywhere in the substance, just closeto the nucleus! (maximum ~10-10 m)

Is the nucleus indivisible? Is it the final indivisible particle?

Is there any other particle in the nucleus?

What is the role of these particles?

How big is the nucleus?

• Size and dimension

The structure of atom

How were the components of the nuclesdiscovered?

Rutherford’s nucleus alteration experiment (1917)Irradiated nitrogen gas with α-particles (He2+):

Internuclear reactions took place!Alteration of chemical elements occurs not only byradioactive decomposition.

HOHeN +=+ HOHeN 11

178

42

147 +=+

Exploring the neutron

Ernest Rutherford

1871-1937

Experiment of Bothe and Becker (1930)They bombarded Beryllium with α-particles, and detected a ray with high penetration ability, which did not diverge in magnetic or in electric field. → Neutral!

Walther Bothe1891-1957

(Nobel-prize in physics,1954)

What is that particle?

Chadwick’s interpretation (1932)Collision of Be and α-particle → new particle is emitted.Same mass as a proton but without any electric charge.

nCHeBe 10

126

42

94 +=+

James Chadwick

1891-1974

(Nobel-prize in physics 1935)

Heisenberg and Tamm (1932)They developed a new nuclear model which includes neutrons, as well.

New meaning is brought to atomic number!

He named this new particle neutron.neutros (greek; neutral)

C126

mass number (A)proton number (Z)or atomic number (charge)

N = A-Z;neutron number

Why is that particle needed?

From the simplest: Hydrogen atom”atom engineering”

H11p+

One proton, nothing more!

RH atom ≈ 10 -10 m;

More complex atom, like He (atomic number = 2)

++

The charged protons repel each other because of the electrostatic Coulomb force.

RH nucleus ≈ 10 -15 m

Size?

The real He atom:atomic number = 2, mass number = 4

+

+• The presence of neutrons does not explain the stability (electrically neutral)!• But they demonstrably stabilize the nucleus.• Some ”glueing effect” should appear! Stronger than the electric repulsion!• Neutrons also take part in creating this force which is not based on electric charge!

What is that force???

He42

00

2 p+ and 2 n0

What are the interactions in the nucleus?

Deficit of mass → binding energy

• The mass of composite nuclei is always less than the total mass of its components (separated protons and neutrons).

• The missing mass value is linearly proportional to the binding energy.

• Energy is disengaged (released), while a nucleus is constructed from free nucleons.

2cmE ⋅Δ=

nucnp mmNmZm −⋅+⋅=Δ )(

mass-energy equivalency rule of Einstein

(Nuclear) Binding energy: is the required energy to removeone nucleon from the nucleus of an atom.

Nuclear force – Strong interaction

Compensates the repulsion of electric charges.

▪ high intensity (strong)▪ short range of interaction (10-15 m)▪ attraction only (always)▪ independent of electric charge

▪ neutrons are also included! ▪ in p-p, p-n, n-n interactions the samemagnitude of force is created

!

10-151038Quantum chromo-

dynamics(QCD)

Strong

∞

∞

range(m)

1General RelativityGravity

1025Quantum electro-

dynamics(QED)

Electromagnetic

Rel. strengthCurrent TheoryInteraction

Interactions (supplement)

Interactions in nature

Gravitation

Electromagnetic force

Strong

Weak

Nuclear models

ZNAAr +=;~ 31

322 ~~ Arsurface

Increasing:nucleon number → mass (number: A)

• radius of atom

• volume of atom ArV ~~ 3

EB

A0

nonlinear!

• surface of atom

Same effect(s) as in the case ofliquid drops!

Increase of nucleon number - effects

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+00

Observations:1. Each of the nucleons is bound with (almost) the same binding energy. (EB

neutron = EBproton !)

2. Total binding energy of the nucleus is proportional to the number of nucleons (A).

3. The volume of the nucleus is linearly proportional to the number of nucleons (A). Hofstaedter (mentioned on previous slide)

Liquid drop model (LDM)incompressible nuclear fluid

This concludes that:→ the density of nucleus is equal for any kind of atom atany point in the nucleus!

4. size-independent density → incompressibility,5. spherical form,6. nucleons interact only with their closest neighbours.

LDM

Based on macroscopic properties (experimental data).Explains: binding energy, mass, stability of nuclei.

Model (1935): created by Carl von Weizsäckerbased on the calculations of Hans Bethe.

( ) 322

31

232 2 −

⋅+−

++⋅+⋅−= AA

ZA

A

ZAAEB ηδγβα

What does that mean???

HundantiPauliCoulombsurfacevolumeB EEEEEE −++++−=

The binding energy is a sum of different energies.Terms explained by classical physics:Nucleons move (exist) in the potential field of the neighbouring nucleons:

→ volume energyNucleons on the surface (outer side) haveless „neighbours” → surface energyElectrostatic energy (charged protons present)

→ Coulomb-energy

LDM - Bethe-Weizsäcker (semi-empirical) mass formula:

http://en.wikipedia.org/wiki/Liquid_drop_modelhttp://en.wikipedia.org/wiki/Bethe-Weizs%C3%A4cker_formula

Memorise:

!

Other terms explained by quantum theory:

Pauli (asymmetry) energy (fermions)

Parameters (α, β, γ, δ, η) are experimentallydetermined – semiempirical model!

Pauli’s Exclusion principle:

forbidden to occupy the same quantum-mechanical state.

Anti-Hund law:

Nucleons - withdifferent spins - like tofill the same energylevel.

LDM

Ep En

anti-Hund (pairing) energy

Maximum: between 55-62!

One nucleons’ binding energy as a function of atomic number

Effect of Coulomb force increases!

The fit is almost good! But...!

The ratio ofsurface and volume (energies)changes! (r2/r3 = 1/r)

Atomic number (atomic mass unit)

Bin

ding

ener

gype

r Nuc

leon

(MeV

)

The model predicts: 63!

What’s wrong with the liquid drop model?

magic numbers:N or Z = 2, 8, 20, 28, 50, 82, 126

These nuclei are more stablethan the LDM predicts.

Atomic number (atomic mass unit)

Bin

ding

ene

rgy

per N

ucle

on (M

eV)

Reason: These atoms contain closed (filled) atomic shells. That phenomenon is not taken into account in the LDM!

The phenomenon is similar to the magic numbers of the electron shells:2, 8,18, 32Halogens have more stable electronstructure because of closed e--shells!

What can we do? Is there a better model?

Atomic shell model (ASM)

Quantum mechanics (QM) can interpret the behavior of the electrons in the electron shell. Certain properties of the nucleus show periodicity.

Is QM able to describe the behavior of the nucleons, too?

Analogy of electron- and atomic shells!

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

• The nucleons Schrödinger equation’s with quantizedparameters (energy, angular momentum, magnetic momentum, spin) → characterise the atomic shells. (spin value: ½, hence Pauli’s-principle is valid)

• Atoms with closed atomic shells are more stable!protons and neutrons separately fill their ownenergy levels

Atomic shell model(sphere symmetric)

ASM

deuteriumH −21

tritiumH −31

heliumHe −42

But several experimental results are not confirmed!

Ep En

hydrogenH −11

0 eV

lowestenergy level

x xy yz z

This theory explains the first three (2,8,20) magic numbers!

The „Unified nuclear model” explains properly in details everynuclear property. This model is not included in the lecture!

SummaryThe components and structure of the nucleus;Strong interactions;Mass deficit;Nucleus models.