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STRUCTURE OF ATOMIC NUCLEUS,
RADIOACTIVITY
14. 11. 2013.
Physical Basis of Biophysics
Nuclear physics
Atomic shells investigation - Quantum physics
Nuclear physics - This science is not closed. There
are more unclarified observations.
The structure of the atom
Democritos,
Dalton,
Thomson,
Rutherford,
Bohr
The word atom has the origin: atomos (
uncuttable (indivisible).
) a Greek word meaning
”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.”
Democritos
Atomic nucleus does not exist!
Atomic models based on experiments: :
Thomsons’ 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.
+
+
+
+
_
Rutherford model (1911)
Discovery of nucleus.
Positively charged nucleus exists and the
electrons move in the substance.
Neutron and proton are not mentioned!
The positive
-particles are diverted because of the
positive charge of the nucleus. (repulsion)
Bohr model (hydrogen atom; 1913)
The electron travels around the nucleus on a circular orbit.
The parameters of orbits are quantized: energy, angular momentum, radius
Neagtively charged electrons→ in electron clouds
(maximum distance~10-10 m)
Positively charged nucleus→ proton and neutron were not known!
The nucleus is uncuttable.
What does an atom consist of?
According to Bohr-Sommerfeld’s model (1915):
Negatively charged electrons → e- clouds
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)
Discovering the atomic nucleus
The stucture of the nucleus
proton
neutron
nukleon
It determines the
chemical element, the
proton number.
The volume of the nucleus is 100 000 –fold smaller than the whole volume
of the atom.
Discovery of proton
Ernest Rutherford in1918
During investigation of the nitrogen gas he observed that the hydrogen can be
detected when alfa-particles hit into the nitrogen gas.
He detected, that the hydrogen can come just from the nitrogen. Nitrogen have
to contain the hydrogen.
The word proton has the origin: protos a Greek word meaning: first (primary)
Exploring the neutron
Rutherford’s nucleus alteration experiment (1917)
Irradiated nitrogen gas with α-particles (He2+):
14
7
N
4
2
He
17
8
O 11H
Internuclear reactions took place!
Alteration of chemical elements occurs not only by
radioactive decomposition.
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 Bothe
1891-1957
(Nobel-prize,1954)
Chadwick’s interpretation (1932)
Collision of Be and α-particle → new particle is emitted.
Same mass as a proton but without any electric charge.
9
4
4
2
Be He
12
6
C
1
0
n
He named this new particle: neutron.
neutros: Greak word, neutral
James Chadwick
1891-1974.
(physical Nobel-prize,
1935.)
Heisenberg and Tamm (1932)
They developed a new nuclear model which includes neutrons, as well.
New meaning is brought to atomic number!
12
6
C
Mass number (A)
Proton number (Z)
or atomic nuber (charge)
N = A-Z;
neutron number
Properties of Particles
Name
Mass (kg)
Electrical
charge(C)
Proton
1,673∙10-27
1,6∙10-19
Electron
9,109∙10-31
- 1,6∙10-19
Neutron
1,675∙10-27
0
Symbol
Relative mass
Relative charge
p+
1
+1
e-
1/1840
-1
n0
1
0
Types of nuclei
According to construction
isotope: same proton number, different neutron number
(11H and 21H)
nuclide: same proton and neutron number
A
Z
A
Z
X
A 4
Z 2
X
X
4
2
He
2
2e
Relative atomic mass
It is a dimensionless physical quantity, the ratio of the average mass of
atoms of an element (from a single given sample or source) to 1/12 of
the mass of an atom of carbon-12.
The amount of substance:
The SI unit for amount of substance is the mole.
The mole is defined as the amount of substance that contains an equal number of
elementary entities as there are atoms in 12 g of the isotope carbon-12. This
number is called Avogadro's number and has the value 6*1023
Molar mass:
M=m/n (g/mol)
Problems
1. How many protons and electrons are in 10847 Ag-atom?
47 proton and 47 elektron
2. How many protons and neutrons are in 35 g 73Li-atom?
3. How many protons and neutrons are in the Ca2+ ion?
From the simplest: Hydrogen atom
„atom engineering”
p+
Size?
RHatom ≈
10
-10
m;
1 proton, nothing more!
1
1
H
RHnucleus ≈ 10 -15 m
More complex atom like: He (atomic number = 2)
+
+
The charged protons repel each other
because of the electrostatic Coulomb force.
The real He atom
0
+
+
Atomic number = 2, mass number = 4
0
2 p+ and 2 n0
4
2
He
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?
What are interaction in the
nucleus?
Nuclear force – strong interaction
Binding energy
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
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.
m ( Z m pr
E
m c
2
N mn ) mnucleus
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)
Interactions
Nuclear models
Increase of nucleon number - effects
+
0
0
Increasing:
nucleon number → mass (number: A)
+
1
• radius of atom
r ~ A 3; A
• volume of atom
3
N Z
V ~r ~ A
• surface of atom
2
surface ~ r ~ A
2
EB
Same effect(s) as in the case of liquid drops!
nonlinear!
V~A
Read this out like: volume is linearly
proportional to the mass number
0
A
3
Liquid drop model (LDM)
incompressible nuclear fluid
Experimental observations:
1. Each of the nucleons is bound with (almost) the same binding energy.
(EBneutron = 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).
Liquid drop model (LDM)
4. size-independent density → incompressibility,
5. spherical form,
6. nucleons interact only with their closest neighbours.
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.
EB
A
A
2
3
Z
A
EB
Evolume Esurface
2
1
3
A 2Z
A
ECoulomb EPauli
2
A
Eanti
2
3
Hund
Binding energy per Nucleon
(MeV)
One nucleons’ binding energy as a function of atomic number
The ratio of
surface and volume (energies)
changes! (r2/r3 = 1/r)
Effect of Coulomb force increases!
Atomic number (atomic mass unit)
Maximum: between 55-60!
The fit is almost good! But...!
The model predicts: 62!
What’s wrong with the liquid drop model?
27
Binding energy per Nucleon (MeV)
magic numbers:
N or Z = 2, 8, 20, 28, 50, 82, 126
These nuclei are more stable than the
LDM predicts.
Atomic number (atomic mass unit)
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!
Reason: These atoms contain closed (filled) atomic shells. That phenomenon is not taken into
account in the LDM!
What can we do? Is there any better model?
Atomic shell model
(sphere symmetric)
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
ASM
Ep
En
0 eV
29
1
1
H hydrogen
2
1
H deuterium
3
1
H tritium
4
2
lowest
energy level
He helium
This theory explains the first three (2,8,20) magic numbers!
But several experimental results are not confirmed!
The „Unified nuclear model” explains properly in details every
nuclear property. This model is not required to know!
Radioactivity
Is the radioactivity a natural process?
Yes
What provokes the transmutation?
The instability of the nucleus!
What kind of utilization do you know?
Nuclear power plant, atom bomb, diagnostics, therapy
Isotopes
There are various form of nucleus (of chemical elements).
Isotopes include the same number of protons but different
numbers of neutrons.
Hydrogen: 1 p+ + different numbers of neutron
- 1: 1H (1 p+)
 Hydrogen - 2: 2H (1 p+ + 1 n0)
 Hydrogen - 3: 3H (1 p+ + 2 n0)
 Hydrogen
hydrogen
deuterium
tritium
The stabiliy of nucleus is defined by the attractive effect between nukleon and repulsive
effect between protons. In case of the stabil isotopes (low atomic number) the number of
protons and neutrons differ slightly.
Unstable nucleus:
The nuclei try to reach more stable state with lower energy
They can emit photons.
Particles are emitted/radiated
Radioactivity
The radiactive radiation is the results of nucleus transmutation.
There are about ~ 40 nature form of radiactive isotopes.
Discovery of radioactivity
Becquerel:
He observed that the uranium caused black spot on non-illuminated
photosensitive plate.
What Becquerel had discovered was that a
piece of mineral which contained uranium could
produce it's image on a photographic plate in
the absence of light.
Pierre Curie (1859-1906) and Marie Curie (1867-1934)
They compared the activity of pure uranium to a uranium ore sample, they
found that the ore was significantly more radioactive than the pure material.
They concluded that the ore contained additional radioactive components
besides the uranium. This observation led to the discovery of two new
radioactive elements which they named polonium and radium.
Binding energy per nucleon
as a function of mass number
Stability of the nucleus
56
26
Fe
Ways to reach Stability
Fission
Nuclear reactors, atomic bomb
Fusion
stars
http://outreach.atnf.csiro.au/education/senior/cosmicengine/sun_nuclear.html
http://www.princeton.edu/~chm333/2002/spring/Fusion/tour1/index.htm
Radioactive radiations
-decay » -radiation
A
Z
A
Z
X
X
A 4
Z 2
X
4
2
He
A 4
Z 2
X
226
88
Ra
Maximal exit speed: 15 000 000 m/s (0,05 c)
Line spectrum (characteristic)
238
92
226
222
210
U , 241
Am
,
Ra
,
Rn
,
95
88
86
84 Po
222
86
Rn
4
2
-decay » -radiation
Negative -decay
Experiment: Curie 1911
n
0
A
Z
X
p
A
Z 1
X
e
νe
e
e
electron
137
55
Cs
νe
137
56
Ba e
Maximal exit speed: 180 000 000 m/s (0,6 c)
Continuous spectrum (antineutrino)
Isotopes:
3
1
14
6
137
55
132
53
40
19
H , C , Cs, I , K
-decay » -radiation
Positive -decay
p
A
Z
X
n0 e
A
Z 1
X
e
νe
positron
e
122
11
Na
νe
22
10
Ne e
isotopes
11
6
22
11
C , Na
-radiation
Side effect of - or -radiation!
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)
22
11
40
132
Na,19
K ,137
Cs
,
55
53 I
-photon
137m
56
Ba
137
56
Ba
m: metastable state
Radiations – base of comparison
External influence not required
Physical and chemical environment has no influence
Ionisation (physics)
Chemical and biological effects
Physical properties:
Activity
Lifetime
Spectrum
Penetration
LET (linear energy transfer)
Comparison
Mean lifetime
222
86
226
88
210
84
238
92
Rn, Ra, Po, U
4 s; 11 days; 138 days; 4,5∙109 years
-
132 3
14
40
53 1
6
19
8 days; 12 years; 5568 years; 1,2∙109 years; 7,6∙10-22 s
+
11
6
I , H , C, K
22
11
C , Na
20 m; 15 h
22
40
137
132
11
19
55
53
2,6 years; 1,2∙109 years; 26 years; 8days
Na, K , Cs, I
Comparison
LET (ions/mm)
Penetration depth, range
Linear
(characteristic)
high
8-10 000
Law
Air: cm
Plexi-glass: mm
Continuous
(because of
anti/neutrino)
average
6-8
Linear
(characteristic)
law
0,1-1
Spectrum
Average
Air: m
Plexi-glass: cm
Lead : mm
High
Lead: cm
Activity(A)
Radioactive transmutation is a random process!
Number of transmutating nuclei in 1 sec.
transmutation = decay
Unit: Becquerel
1 Bq = 1 transmutation /sec.
Attention! Radioactive ”decomposition”
does not mean that the atom disappears!
Do not use ”disintegration” for the process
Old unit: Curie (1 Ci = 3.7 ∙ 1010 Bq)
Stable isotope
Radioactive isotpe
Daughter atom
Decay law
N(0) : number of radioactive nuclei at
the begining
N(t) : number of remaining radioactive
nuclei at any moment ”t”
Decay constant ( ):
Characterises
the
rate
of
decomposition.
Defines
the
probability of transmutation of
one nucleus.
A
Number of remaining
radioactive nulei
N(0)
T1
N (t ) N ( 0) 2
2
N(0)/2
N(0)/e
T1/2
N (t )
Mean lifetime( ):
Reciprocal of the decay constant.
t
1
time
t
N (t )
N ( 0) e
Half life– mean lifetime
The time required for ½ the amount of a radioactive material to
disintegrate.
Phosphorus-32 radioactively decays
to form Sulfur-32
Half life 32P = 14 days
t
N (t )
N ( 0) 2
T1
t
N (t ) N ( 0) e
t
2
2
T1
t
2
1
ln 2
T12
e
1,443 T12
Problems
Half life
1. The intensity of the radiactive sample is 8300 cpm. After15 days the
intensity is 6457 cpm. Calculate the half-life!
41,4 days
Activity
2. When you make an experiment with 86Rb, the Geiger Müller-detector shows
21000 cpm count rate at a distance of 2 cm from the test tube. What would be
the distance from the tube, when the detector shows 840 cpm?
The number of detected particles is inversely
proportional to the square of the distance.
N(far)= N(near)/(r2/r1)2
10 cm
Homework
1. How many protons and neutrons are in 5 g
40
19
K –atom?
s
s
2. How many is the decay constant of the radioactive sample is
the half-life is 3 years.
1
1,443 T12
1
ln 2
T12
λ=0.23
3. Determine the activity of unknown radioactive Cd isotope if
the activity is 1540 Bq after 21 days and the half-life is 4 days!
Thank you for your attention!