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:
X
A Z A: Number of Nucleons Z: Number of Protons (Electrons)
0
• Example: Carbon C; Neutron n; Electron e; Proton p
12 1
1 0
1 1
-1
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,
15 m)(56)1/3 = 4.6 fm
R = RoA1/3 = (1.2
10 27 kg) = 9.3
26 kg
m = (56 u)(1.66
⇥ 10
10
⇥
V =
⇡R3 =
15 m)3 = 4.1
43 m3
⇥ (4.6
10
10
4 3
⇥
⇢ =
=
17 kg/m3
10
approximate mass, and density of an iron nucleus.
Nucleus is 1013 times the density of iron
4 3 m V
9.3 4.1
⇥ 26 kg 43 m3 = 2.3
⇥
10 10
⇥ ⇥
Magnetic Moments
• Like electrons, nucleons have 1/2-integer spin angular momentum,
s(s + 1)
S = ~ • The z-component is itself a quantum number as electron spin:
p Sz =
~
1 2
±
obeying the same relations as electron spin:
• The magnitude of the total angular momentum J of the nucleus is also
j(j + 1)
J = ~
p
neatly quantized as:
(mj = 0; ±1; ±2;…; ±j)
with quantized z-component: Jz = mj~ • 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
µN =
= 2.7928 µN
eh 2mp
= 1.9130 µN
msz|
|
msz|
|
the case of a nucleus, the quantity of magnetic moment is nuclear magneton: Magnetic moment for the proton and neutron:
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
Z M )c2 A
EB = mc2 = (ZMH + N mn
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 MH is the mass of a hydrogen atom, Z M )c2 A not just its proton, also 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
He
nuclei
:
particles α
−
+
4 2 e :
e or
: high
energy
photons
particles β rays γ
A positron (e+) is the antiparticle of the electron (e-)
Alpha Decay
4)
A Z X
2 He
(A (Z
2) Y +4
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
!
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
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:
t
=
dt =
ln
=
t =
N = Noe
dN N
)
)
N No
proportional to the number of atoms available to decay, e.g.
Activities and Half-lives
• To find the half-life, just determine when
t =
e
N =
1 2
No 2
t = t1/2 =
ln2
and
• 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.
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)
• The quantity 1/λ is called the mean lifetime.
Example
57Co nuclei do the source contain? (c) What will be the activity after 1 year?
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
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 =
t =
R = Roe
• 14C decays to 14N by emitting a beta.
ln(R/Ro)
)
T1/2 of 14C is 5730 years
Example
Radiocarbon dating. The isotope 14C via beta-minus decay to 14N with a half-life of 5730 years. Before 1900, the activity per unit mass of atmospheric carbon due to the presence of 14C averaged about 0.255 Bq per gram of carbon. (a) What fraction of carbon atoms were 14C? (b)
In analyzing an archaeological specimen containing 500 mg of carbon, you observe 174 decays in one hour. What is the age of the specimen?
Nuclear Reactions
• A nuclear reaction is rearrangement of nuclear components due to
bombardment by a particle rather than a spontaneous natural process.
• The difference in masses before and after the reaction corresponds to
the reaction energy Q.
• Nuclear reactor is a system in
which nuclear chain reaction is used to liberate energy
Nuclear Fission
• Nuclear fission is a decay process in which an unstable nucleus splits
into two fragments (the fission fragments) of comparable mass.
Nuclear Fusion
• In a nuclear fusion reaction, two or more light nuclei fuse to form a
large nucleus.
