Download Chapter 12 Nuclear Physics

Chapter 12. Nuclear Physics
Chapter 12
Nuclear Physics
§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
1. The electrical charges of nucleus:
Nucleus is composed of protons and neutrons. Proton has a portion of positive
charge which is the same as the electronic charge and neutrons have no electronic
charges. Nucleus has positive charges and it is rotated. Because of this, it has angular
momentum and magnetic moment. The smallest unit of charges is the integer
multiples of electronic charge. 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. The unit
of atomic masses is defined as the carbon atom’s mass divided by 12, denoted by u.
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 (Z) and neutrons (N). Therefore,
AZ N
(12.1)
where Z is atomic number which is the number of electron and N is the number of
neutrons in the atom.
Atomic mass unit (u)  1.66054  10 27 kg
(12.2)
m p  1.007277u
(12.3)
mn  1.008655u
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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
(12.4)
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 3 4 3
V
r
r0 A 4r0
3
3
(12.5)
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 nuclear is
3(1.67  10 27 kg)
n 
 2.3  1017 kg / m 3
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. The force has four 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, n-p 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
m x  Z  m p  ( A  Z )mn
(12.6)
Unfortunately, the experiments show that the nucleus mass is less the sum on RHS of
the above equation and the difference is m, called the mass defect. Relativity points
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Chapter 12. Nuclear Physics
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  m x
(12.7)

(12.8)
is the mass defect. DE 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.
§12.2 The decay type of the atomic nucleus
A single nuclear species with same Z and N is called nuclide. Nuclide 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.
1. 
decay
The heavy nucleus with its mass number A>209 could emit a particles. The decay
process can be written as
A
Z
X AZ42Y 24  Q
(12.9)
where X is parent or radioactive nucleus, Y is daughter nucleus,  is Helium’s nucleus
and Q is the decay energy.
No nucleus with A greater than 209 is stable. The stability of nuclei can be
understood qualitatively on the basis of the nature of the nuclear force and the
competition between the attractive nuclear force and the repulsive electrical force. As
pointed out previously, the nuclear force favors pairs of nucleons, and pairs of pairs.
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 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, compared with the attractive nuclear 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:
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Medical Physics
A
Z
X Z A1Y   -    Q
  decay
A
Z
X Z A1Y       Q
  decay
A
Z
X   -  Z A1Y    Q
electron capture
3.  decay and inner transmission
Most of the daughter nuclei after α or β decay are in excited state and release their
energies in  rays, and then leave them 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.
§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:
(12.10)
N  Nt
Where  is 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 0 e  t
•
(12.11)
The half-life (半衰期)
t = T, N = N0/2
So we have
1
2
N 0  N 0 e  T
 e T  2
T  ln 2  T 
0.693

The unit of half-life is minute, hour, day or year.
•
The radioactivity
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(12.12)
Chapter 12. Nuclear Physics
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
I 
  N 0 e t   N 0 e t
dt
dt
 N  I 0 e  t
(12.13)
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
mCi
(microcurie)
(12.14)
It is known that they are similar to meters used.
Example 12-1: The activity of radium: the half-life of the radioactive nucleus
226
86
Ra 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 3 years )(3.15  10 7 s / year )
 5.05  1010 s
So the decay constant can be obtained as:
0.693
0.693


 1.4  10 11 s 1
T
5.05  1010 s
We can calculate the activity of the sample at t = 0 using
dN
  N 0 e  t | t  0   N 0
dt
 1.4  10 11 s 1 3.0  1016
I0  



 4.2  10 5 Bq / s  11.1Ci
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§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 interactions between particles
• Gravitational interaction,
• Weak interaction,
• Electromagnetic interaction,
• Strong interaction
• Unification of the four interactions
12. 4.3 The classification of particles
• Photons
• Leptons (轻子) and lepton numbers
• Hadrons (强子): Any of a class of subatomic particles that are composed
of quarks and take part in the strong interaction.
12.4.4 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.
• Photon transmits the electromagnetic force,
• Graviton transmits the gravitational force,
• Intermediate vector boson transmits the weak interaction, and
• Gluon transmits the strong interaction.
Problems
1. Try to explain that
16
O12 C 4 H e is impossible.
2. Calculate the emitting energy for two 2H molecules combining one 4H molecule.
3. If the emitting energy of two hydrogen atoms combining one hydrogen molecules
is 4.37 eV, try to calculate the mass defect due to this process.
4. Calculate the nuclear binding energy and the nuclear average binding energy for
deuteron and helium?
5. The half-life of 131I (iodine) is 8.04d. If it is measured at 9:00 am on 12th when its
radioactivity was 5.6106 Bq, how much will it be at 3:00 pm on 30th in the same
month?
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Chapter 12. Nuclear Physics
6. There are two kind of radioactive nuclides whose half-life are 8d and 6h
respectively. Suppose that their radioactivities are the same, find the radio of the
two radioactive nuclide numbers.
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