Download Chapter 12 Nuclear Physics

Chapter 12
Nuclear Physics
(June 10, 2005)
Error corrections:
Chapter 11, question 6, find the
“intensity”, not “density”
Summary to the last lecture
1. The fundamental principles of laser
• Atomic energy levels: ground, metastable
and excited states
• Absorption; spontaneous emission,
stimulated emission.
• Atomic distribution and population
inversion
• Optical Resonator
2. The characteristics of laser
• Good directionality
• High brightness and high intensity.
• Good monochromatic
• Good coherence (time & spatial 相干性)
• Good polarization (偏振)
12.1 The basic properties of
nucleus
In proceeding chapters we have frequently
made use of the fact that every atom contains
a massive, positively charged nucleus, much
smaller than the overall dimensions of the
atom but nevertheless containing most of the
total mass of the atom. It is instructive to
review the earliest experimental evidence for
the existence of the nucleus.
It is well known that an atom has a nucleus
in the center of the atom. The most obvious
feature of the atomic nucleus is its size, of the
order of 20,000 to 200,000 times smaller than
the atom itself. Although the “surface” of a
nucleus is not a sharp boundary,
experiments determined an approximate
radius for each nucleus. The radius is found
to depend on the mass, which in turn
depends on the total number A of neutrons
and protons, usually called mass number.
12.1.1 the structures of nucleus (核子)
1. The electrical charges of nucleus:
Nucleus is composed of protons and neutrons.
Proton （positive charge） and neutrons （no
electronic charges）.
Nucleus has positive charges and it rotates.
Because of this, it has angular momentum and
magnetic moment. The total number of
positive charges, the number of protons, is
denoted by Z which is also celled the atomic
number.
2. Nuclear masses:
Mass of an atom includes the mass of
electrons and the mass of nucleus.
Carbon' s atomic mass
Atomic mass unit (u) 
12
As the mass of a proton or a neutron is very
close to 1u, the atomic mass number A is equal to
the total number of protons and neutrons.
Therefore,
A=Z+N
Atomic mass number
A
Z
Number of neutrons
X
Atomic number
1eV  1.602 10
1
1
,  ,
2
1
19
16
8
Symbol of atoms
J
, e,
4
2
23
11
Na
Atomic mass unit (u)  1.66054 1027 kg
m p  1.007277u
1uc  1.66054 10
 931.5MeV
2
mn  1.008655u
27
c  1.49242 10
2
10
J
12.1.2 Nuclear properties
1. The size and density of the nucleus:
The radii of most nuclei are represented
fairly well by the empirical equation
r  r0 A
1
3
1 fm = 10-15 m
r0 is an empirical constant 1.2×10-15m,
the same size for all nuclei. The density of
nucleon could be found as follows:
M
M
A m
3m




3
4
4
V
4

r
3
3
0
r
r0 A
3
3
Where m is the mass of a nuclear such
as proton or neutron which is given as
1.67  10-27kg. So the density of the
nucleus is
27
3(1.67 10 kg)
17
3
n 

2
.
3

10
kg
/
m
15
3
4 (1.2 10 m)
2. Nuclear forces and nuclear energy
levels:
The force of making the protons and
neutrons together is obviously not
electromagnetic force as neutrons are
charge free and it is not the gravitational
force either. Experiments show that such a
force is a special interaction force which is
called nuclear force.
• Nuclear force properties:
(1). It is a “short distance force” as its
effective distance is about 10-15m and out of
this range it reduces to zero sharply;
(2). The force is the strongest force we have
observed so far;
(3) the force has a feature of saturation, the
nucleus can interact only with its nearest
neighbor;
(4) the interaction of nuclear force does not
depend on charged condition of nuclei.
That is that interaction forces from n-n, np and p-p are almost the same.
Nuclei are same as the atoms and they also
have discrete energy levels (angular
momentum and magnetic moment). Energy
transmission can be also happened under
the surrounding perturbations.
12.1.3. Nuclear binding energy and
mass defect (亏损）
Nucleus is composed of nucleons (核子)
and its mass should be equal to the sum of
the mass of all the individual nucleon
composing the nucleus. If the masses of
the nucleus, the proton and the neutron are
denoted by mx, mp, mn respectively, we
should have such an equation
mx  Z  m p  ( A  Z )mn
A
Z
X
Unfortunately, the experiments show that the
nucleus mass is less than the sum on RHS of
the above equation and the difference is m,
called the mass defect. Relativity points out
that if there is mass defect, there must have
energy changes. The difference of energy and
the difference of the mass has the following
relation.
E  (m)c
2
Where

m  Zm p  ( A  Z )mn  mx

is the mass defect. E is called the
nuclear binding energy. Such an energy
was emitted when the nucleus was
created. The higher the binding energy
is, the more condensed and the more
stable the nucleus is. This is why the
nuclei are stable.
Brief Review to the last lecture
• what does the symbol
A
Z
X mean?
• what are the nuclear force properties? ,
• what is the mass defect?
• what is the nuclear binding energy?

m  Zm p  ( A  Z )mn  mx
E  (m)c
2

12.2 The decay types of the
atomic nucleus
Nuclide (核素) has two big classes. One of
them is radioactive nuclide and the other is
stable nuclide. The radioactive nuclide can
emit particle rays and be changed into another
nuclide. This phenomenon is regarded as
nuclear decay （原子核衰变）.
1.  decay
The heavy nucleus with its mass number
A>209 could emit  particles. The decay
process can be written as
A
Z
X
Radioactive (or
parent) nucleus
Y   Q
A 4
Z 2
4
2
Kinetic
Decay energy
Nucleus of Helium
Daughter nucleus
A > 209  unstable
Stability is from the attractive nuclear
force and the repulsive electrical force.
nuclear force favors pairs of nucleons,
In the absence of electrical interactions,
the most stable nuclei would be those
having equal numbers of neutrons and
protons, N = Z.
The electrical repulsion shifts the balance
to favor (like) greater numbers of
neutrons,
but a nucleus with too many neutrons is
unstable because not enough of them are
paired with protons.
A nucleus with too many protons has too
much repulsive electrical interaction to
be stable.
2.  decay
 Decay denotes the parent nucleus
becomes another nucleus spontaneously
with its mass number unchangeable. Of
course this decay is a decay to emit an
electron. Such a decay has three kinds of
forms that can be described by the
following equations:
A
Z
X Y  e   e  Q
 decay
A
Z
X Y  e   e  Q
 decay
A
Z
X  e  Y  e  Q
electron capture
A
Z 1
-

A
Z 1
-
A
Z 1


3.  decay and inner transition
Most of the daughter nuclei after α or β
decay are in excited state and release
their energies in  rays, and then leave
their in ground state. This phenomenon
is called  decay. In this process, a 
photon is emitted.
The inner transmission is the above
phenomenon but no  photon
emission. The energy was transferred
to the electrons outside the nucleus,
the electron may become an free
electron, leave the nucleus in a
ground state, companied by x-rays
generation
12.3 The nuclear decay law
•
The decay law
If a radioactive sample contains N
radioactive nuclei at some instant, it is found
that the number of nuclei, N, that decay in a
small time interval t is proportional to N:
N = N t
Where  is a constant called decay constant.
The negative sign signifies that N decrease with
time; The value of  for any isotope determines
that rate for which that isotope will decay.
The decay rate is defined as the number
of decay per second.
dN
N
dN
 lim
 N 
 dt
dt
N
t 0 t
dN
 N    dt  ln N  t  C
The decay Law is
N  N 0e
 t
• The half-life (半衰期)
t = T, N = N0/2
1
2
N 0  N 0e
T
 T
N0
N  N 0e
 t
1
N0
2
t
T
e 2
0.693
T  ln 2  T 

The unit of half-life is minute, hour, day
or year.
• The radioactivity (放射性强度)
The radioactivity is defined as the nuclear
number of decay in unit time. It is
sometimes called radioactive intensity or
decay rate or activity, denoted by I.


dN
d
 t
 t
I 

N 0 e  N 0 e
dt
dt
 t
 N  I 0 e
The units of radioactivity are initially
in Becquerel (Bq).
1Bq = 1 decay / s
(Bq = Becquerel)
1 Ci = 3.7  1010 Bq (Ci = Curie)
= 3.7  104 MBq (M=mega ~106)
= 3.7  10 GBq (G=Giga ~ 109)
= 3.7  10-2 TBq (T = Tera ~ 1012)
= 103 mCi (millicurie)
= 106 Ci (microcurie)
It is known that they are similar to meters used.
Example 12-1: The activity of radium: the halflife of the radioactive nucleus 22686Ra is 1.6  103
years. If the sample contain 3.0  1016 such
nuclei, determine the activity at this time.
Solution: first, let us convert the half-life to
seconds
T  (1.6 10 years )(3.15 10 s / year )
3
7
 5.05 10 s
10
So the decay constant can be obtained as:
0.693
0.693
11 1



1
.
4

10
s
10
T
5.05 10 s
We can calculate the activity of the sample
at t = 0 using
dN
 t
I0  
 N 0e |t 0  N 0
dt
11 1
16
 1.4 10 s 3.0 10


 4.2 10 Bq  11.1Ci
5

12.4 Introduction to
Elementary Particles
12. 4.1 The basic properties of particles
• Masses,
• charges,
• spin,
• magnetic moment
• Average life-time.
12. 4.2 The interaction between particles
• Gravitational interaction,
• Weak interaction,
• Electromagnetic interaction,
• Strong interaction
• Unification of the four interactions (later)
12. 4.2 The classification of particles
• photons
• Leptons (轻子) and lepton numbers
Name
e-, e
e+, e
-, 
Le
1
-1
0
L
0
0
1
L
0
0
0
+, 
-, 
+, 
0
0
0
-1
0
0
0
1
-1
Y  e  e  Q
A
Z
X
A
Z
X Y  e   e  Q
A
Z
X  e  Y  e  Q
A
Z 1
-

A
Z 1
-
A
Z 1
n  p  e  e

Hadrons (强子): Any of a class of
subatomic particles that are composed of
quarks and take part in the strong
interaction.
Mesons (介子)
• Hadrons
Nucleus (核子)
(强子) Baryons ( 重子)
Hyperons (超子)
Vector Boson (矢量玻色子):
Any of the elementary particles that mediate
one of the four fundamental forces or
interactions is called vector Boson.
(1) photon and the electromagnetic force,
(2) graviton and the gravitational force,
(3) intermediate vector boson and the weak
interaction, and
(4) gluon and the strong interaction.