Xem mẫu
- Nuclear Physics
Pham Tan Thi, Ph.D.
Department of Biomedical Engineering
Faculty of Applied Sciences
Ho Chi Minh University of Technology
- Fundamentals of Atom and Nuclei
- Nuclides and Isotopes
• Electron and nucleon masses (12C nucleus is defined to have u = 12.00)
Proton: mp = 1.007276 u
Neutron: mn = 1.008665 u
Electron: me = 0.000548580 u
• The atomic number Z is the number of protons in the nucleus. The
neutron number, N, is the number of neutrons in the nucleus. A = Z + N
• A nuclide is an atom of a particular structure. Each element has
nucleus with a specific number of protons.
• Nuclide notation:
A
ZX
A: Number of Nucleons
Z: Number of Protons (Electrons)
12 1 0 1
• Example: Carbon 1C; Neutron 0n; Electron -1e; Proton 1p
- Fundamentals of Atom and Nuclei
✴ The number of nucleons A (also called the mass number) is the total
number of protons and neutrons in the nucleus. The nucleon mass is
measured in atomic mass unit, u, slightly less than the mass of the
proton:
1 u = 1.6605 x 10-27 kg
✴ The radius of most nuclei is given by R = RoA1/3, where Ro is
experimentally determined as Ro = 1.2 x 10-15 m (1.2 fm)
✴ All nuclei have approximately the same density.
✴ Example: Common iron nuclei has mass number 56. Find the radius,
approximate mass, and density of an iron nucleus.
R = Ro A1/3 = (1.2 ⇥ 10 15
m)(56)1/3 = 4.6 fm
27 26
m = (56 u)(1.66 ⇥ 10 kg) = 9.3 ⇥ 10 kg
4 3 4 15
V = ⇡R = (4.6 ⇥ 10 m)3 = 4.1 ⇥ 10 43
m3
3 3
m 9.3 ⇥ 10 26
kg 17 3
Nucleus is 1013 times
⇢= = 43
= 2.3 ⇥ 10 kg/m the density of iron
V 4.1 ⇥ 10 m3
- Magnetic Moments
• Like electrons, nucleons have 1/2-integer spin angular momentum,
obeying the same relations as electron spin:
p
S=~ s(s + 1)
• The z-component is itself a quantum number as electron spin:
1
Sz = ± ~
2
• The magnitude of the total angular momentum J of the nucleus is also
neatly quantized as: p
J =~ j(j + 1)
with quantized z-component: Jz = mj ~ (mj = 0; ±1; ±2;…; ±j)
• When A is even, j is an integer; but A is odd, j is a half-integer
• Associated with the nuclear angular moment is a magnetic moment. In
the case of a nucleus, the quantity of magnetic moment is nuclear
magneton:
eh Magnetic moment for the proton and neutron:
µN =
2mp |msz | = 2.7928 µN |msz | = 1.9130 µN
- NMR and Magnetic Resonance Imaging
Nuclear Magnetic resonance and MRI use strong magnetic field to align
the nuclear spins, then flips the spins with radio waves. When the radio
waves cease, the spins flip spontaneously and emit radio photons that
are measured.
- Nuclear Binding Energy
The mass of the 12C atom, made up of 6
protons and 6 neutrons, defines the
mass unit u, i.e. it has a mass of
exactly 12 u. The individual masses
of the protons and neutrons is
6(1.007276 u) + 6(1.008665 u) =
12.095646 u. The difference, 0.0956
u, when converted to energy E = mc2,
is the binding energy EB of the
nucleus. It is convenient to use the
mass-energy equivalent of c2, which
is 931.5 MeV/u, so that 0.0956 u =>
89.1 MeV is the binding energy of 12C.
It is the energy that must be added to
separate the nucleons. The quantity
EB/c2 is called the mass defect.
EB = mc2 = (ZMH + N mn A
Z M )c2
MH is the mass of a hydrogen atom,
EB = mcnot
2
= just
(ZMits
H +proton,
N mn A also
Z M )c
2
includes
the electrons of the atom
- Nuclides and Isotopes
• Isotopes are nuclei which have the same number of protons but
different numbers of neutrons
- Stable Nuclei and Unstable Nuclei
Stable Nuclei:
• Z:N ≈ 1:1 when Z is small (light)
• Z:N ≈ 1:1.5 when Z is large (heavy)
Unstable Nuclei:
Most nuclei out of these ranges are
unstable
- Radioactive Decay
Radioactive decay is the process by which an unstable atomic nucleus
losses its energy by emitting radiation.
• Parent nuclei decay to daughter ones having a higher nuclear
binding.
• An atom is radioactive when its nucleus is experienced re-arranged.
• Radioactive decay is a process of emitting radiation.
• Energy releases when decaying.
- Radioactivity
• Unstable nuclei decay to more stable nuclei
• An isotope can emit 3 types of radiation in the process
α particles : 42 He nuclei
β particles : e − or e +
γ rays : high energy photons
A positron (e+) is the antiparticle
of the electron (e-)
- Alpha Decay
An alpha particle (α) is a 4He nucleus, which is very stable. Large
nuclei can decay by splitting into a smaller nucleus and an alpha
particle, such as
A (A 4) 4
ZX !(Z 2) Y +2 He
Alpha decay is possible whenever the parent nuclide is more
massive than the sum of the two daughter products.
- Beta Decay
• In a nucleus with too many protons or too many neutrons, beta decay
takes place when one of the protons or neutrons is transformed into
the other.
• The number of nucleons, A, does not change after decaying process;
the number of protons is increased or decreased.
• There are three types of beta decays: beta-minus, beta-plus and
electron capture.
- Gamma Decay
• A decaying process in which an unstable nucleus dissipates excess
energy by a spontaneous electromagnetic process is called gamma (γ)
decay.
• No particles are ejected from the nucleus when it undergoes this type
of decay.
• Gamma ray has the same characteristic as X-ray does, but their origins
are different:
✴ X-ray originates from electromagnetic interaction process
✴ Gamma ray stems from changing energy levels
- Characteristics of Decays
- Activities and Half-lives
• The half-life is the time for the number
of radioactive nuclei to decrease to
one-half of their original number.
• Because the number of decays is
proportional to the number of atoms
available to decay, e.g.
dN = N dt
(minus sign indicates a loss), the number
of remaining nuclei decrease
exponentially. The solution to the above
equation is found by re-arranging and
integrating:
dN N t
= dt =) ln = t =) N = No e
N No
- Activities and Half-lives
• To find the half-life, just determine when
No t 1
N= and e =
2 2
ln2
t = t1/2 =
• If you start with No nuclei, after a half-life
you will have No/2, and after another half-
life you will have No/4, etc.
• The quantity 1/λ is called the mean lifetime.
An established unit of radioactivity (-dN/dt) is called Curie:
1 Ci = 3.70 x 1010 decay/s
In SI units, 1 decay/s is called Becquerel (Bq)
- Example
Activity of 57Co. The isotope 57Co decays by electron capture to 57Fe
with a half-life of 272 d. The 57Fe nucleus is produced in an excited
state, and it almost instantaneously emits gamma rays that we can
detect.
(a) Find the mean lifetime and decay constant for 57Co
(b) If the activity of 57Co radiation sources is now 2.00 µCi, how many
57Co nuclei do the source contain?
(c) What will be the activity after 1 year?
- Radioactive Carbon Dating
• Cosmic radiation protons blast nuclei in
the upper atmosphere, producing
neutrons which in turn bombard
nitrogen, the major constituent of the
atmosphere. This neutron bombardment
produces the radioactive isotope 14C.
The radioactive 14C combines with
oxygen to form CO2 and is incorporated
into the cycle of living things.
• The 14C forms at a rate which appears to
be constant, so that by measuring the
radioactive emissions from once-living
matter and comparing its activity with
equilibrium level of living things, a
measurement of the time elapsed can be
made.
• Dead organisms/things do not absorb
14C.
t ln(R/Ro )
R = Ro e =) t = • 14C decays to 14N by emitting a beta.
T1/2 of 14C is 5730 years
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