structure of atom nucleus - pécsi...
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Structure of atom nucleus
Biophysics lectures
november 2013
József Orbán
http://biofizika.aok.pte.hu/en/
3
Philosophers / scientists Timeline
Schrödinger Aristoteles Dalton Bohr J.J.Thompson
Fermi Einstein and Szilárd Teller 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
4
The atomic models from the viewpoint of the nucleus
5
+ _
_ +
+ +
+
The word atom has the origin: atomos (atomos),
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. The
positive charge is spread in a ”large” volume.
+ _
_ +
+ +
+
+ +
+ +
+ R0 = 1.4 · 10-15 m
Rutherford model (1911)
Positively charged nucleus
exists and the electrons
move in the substance.
Neutron and proton are not
mentioned!
experimental setup
a-particles
a
6
What does an atom consist of?
According to Bohr’s model (1913):
• Negatively charged electrons → e- cloud
• Positively charged nucleus → proton and neutron were
not known!
• Spatial connection between the nucleus and electron: it
can not appear everywhere in the substance, just close
to 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?
7
Discovering the atomic nucleus
8
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 1
0
12
6
4
2
9
4 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)
C12
6
mass number (A)
proton number (Z) or atomic number (charge)
N = A-Z;
neutron number
Why is that particle needed?
10
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???
He4
2
0 0
2 p+ and 2 n0
11
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
nucnp mmNmZm )(
mass-energy equivalency rule of Einstein
(Nuclear) Binding energy: is the required energy to remove
one nucleon from the nucleus of an atom. (c: speed of light)
12
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 same
magnitude of force is created
!
13
Interaction Current Theory Rel. strength range
(m)
Strong
Quantum chromo-
dynamics
(QCD)
1038 10-15
Electromagnetic
Quantum electro-
dynamics
(QED)
1025 ∞
Gravity General Relativity
1 ∞
Interactions (supplement)
14
Nuclear models
15
ZNAAr ;~ 31
32
2 ~~ Arsurface
nucleon number → mass (number: A)
• radius of atom
• volume of atom ArV ~~ 3
EB
A 0
non-linear!
• surface of atom
Same effect(s) as in the case of
liquid drops!
Increasing nucleon number - effects
+
+
0 0
16
Observations:
1. Each of the nucleons is bound with (almost) the same
binding energy. (EBneutron = EB
proton !)
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 at
any point in the nucleus!
4. size-independent density → incompressibility,
5. spherical form,
6. nucleons interact only with their closest neighbours.
17
LDM
Based on macroscopic properties (experimental data).
Explains: binding energy, mass, stability of nuclei.
Model (1935): created by Carl von Weizsäcker
based on the calculations of Hans Bethe.
3
22
3
1
2
3
22
AA
ZA
A
ZAAEB a
What does that mean???
HundantiPauliCoulombsurfacevolumeB EEEEEE
20
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 of
surface and volume (energies)
changes! (r2/r3 = 1/r)
Atomic number (atomic mass unit)
Bin
din
g e
nerg
y p
er
Nucle
on
(MeV
)
The model predicts: 62!
62Ni
21
What’s wrong with the liquid drop model?
magic numbers:
If N or Z = 2, 8, 20, 28, 50, 82, 126
These nuclei are more stable than
the LDM predicts.
Atomic number (atomic mass unit)
Bin
din
g e
nerg
y p
er
Nucle
on (
MeV
)
Reason: These atoms contain closed (filled) nuclear shells.
This phenomenon is not taken into account in the LDM!
The phenomenon is similar to the
magic numbers of the electron shells:
2, 8,18, 32
Halogens have more stable electron
structure because of closed e--shells!
What can we do? Is there a better model?
23
Bartlet, Elsasser, 1934: „independent particle model”
Jensen and Göppert-Mayer, 1949: atomic shell model
• The nucleons Schrödinger equation’s with quantized
parameters (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 own
energy levels
Atomic shell model (sphere symmetric)
24
ASM
deuteriumH 2
1
tritiumH 3
1
heliumHe4
2
But several experimental results are not confirmed!
Ep En
hydrogenH 1
1
0 eV
lowest
energy level
x x y y z z
This theory explains the first three (2,8,20) magic numbers!
The „Unified nuclear model” explains properly in details all
nuclear property. This model is not included in the lecture!
oxigenO16
8
25
Electron - J. J. Thomson (1897)
Proton - E. Goldstein (1900)
Nucleus - E. Rutherford (1911)
Neutron - James Cheidwick (1932)
Quarks - Leon Lederman (1977)
Radioactivity
Types of radiation
University of Pecs, Department of Biophysics
november 2013
József Orbán
27
Is the radioactivity a natural process?
Yes it is! Since the Big Bang...
What induces the transmutation/decay?
What kind of application(s) do you know?
The instability of the nucleus!
Nuclear power plant, atom bomb, diagnostics, therapy
Binding energy per nucleon as a function of mass number
Fe56
26
All atom (nucleus) wants to get to the most stable conformation
either by increasing or decreasing nucleon number.
General
Laws
N=Z
Neutron-proton ratio
increases to ~1.5!
Nuclei tend to get the most stable „structure”! 5626Fe
fusion
fission - -decay
-decay
Iron valley
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/modes.php
Ways to reach Stability
Fission Fusion
http://www.princeton.edu/~chm333/2002/spring/Fusion/tour1/index.htm
http://outreach.atnf.csiro.au/education/senior/cosmicengine/sun_nuclear.html
Nuclear reactors, atomic bomb stars
a-decay » a-radiation
HeXX A
Z
A
Z
4
2
4
2
a
XX A
Z
A
Z
4
2
PoRnRaAmU 210
84
222
86
226
88
241
95
238
92 ,,,,
Maximal exit speed: 15 000 000 m/s (0.05 c)
Line spectrum (characteristic)
a4
2
222
86
226
88 RnRaA: atom number
Z: proton number
-decay » -radiation
e
A
Z
A
Z eXX
1
eνepn 0
Negative -decay
Maximal exit speed: 180 000 000 m/s (0.6 c)
Continuous spectrum (antineutrino)
Experiment: Curie 1911
Theory: Enrico Fermi, 1934
eνeBaCs 137
56
137
55
electron
eνeNeNa 22
10
122
11
eνenp 0
Positive -decay
-decay » -radiation
KICsCH 40
19
132
53
137
55
14
6
3
1 ,,,,
NaC 22
11
11
6 , isotopes
- isotopes
e
A
Z
A
Z eXX
1 positron
-radiation Side effect of a- or -radiation!
ICsKNa 132
53
137
55
40
19
22
11 ,,,
Electromagnetic radiation
(-photon)
f>1019 Hz, and E>100 keV
Created at energy transitions of
nucleus, from excited state to
ground state.
Propagates at light speed
Line spectrum (characteristic)
BaBam 137
56
137
56
m: metastable state
-photon
electron
Radioactivity
What type of detectors are used to detect radioactive radiation?
a → Wilson-type cloud chamber
→ Geiger Müller counter
→ Scintigraph
Why do we need so many types of detectors?
They interact differently with matter.
http://en.wikipedia.org/wiki/Cloud_chamber
Radiations – base of comparison
• Activity
• Life time
• Spectrum
• Penetration depth and
• LET (linear energy
transfer)
• External influence not
required
• Physical and
chemical environment
has no influence
• May induce ionisation
(physics), then
• Chemical and
biological effects
Physical properties:
Activity (A)
Number of transmutating nuclei in 1 sec.
transmutation = decay
Unit: Becquerel
1 Bq = 1 transmutation/sec (tps).
Old unit: Curie. (1 Ci = 3,7 · 1010 Bq)
Stable isotope
Radioactive isotope
Daughter atom
Attention! Radioactive ”decomposition”
does not mean that the atom disappears!
Do not use ”disintegration” to name the
process!
Radioactive transmutation is a random process!
http://en.wikipedia.org/wiki/Radioactive_decay
Law of decomposition - activity
t
t
t eNN
)0()(
t1
21
2)0()(
T
t
t NN
elapsed time
Number of remaining
radioactive nuclei
N(0)
N(0)/2
T1/2
N(0)/e
t
N(0) : number of radioactive
nuclei at the begining
N(t) : number of remaining
radioactive nuclei at any
moment ”t”
Mean lifetime (t):
Reciprocal of the decay constant.
Decay constant ():
Characterises the rate of
decomposition.
Defines the probability of
transmutation of one nucleus.
)(tNA
Half life (time) – mean lifetime
t
t
t eNN
)0()(
21
21
443,12ln
1T
T
t
21
2)0()(
T
t
t NN
t
tT
t
e
21
2