The atomic nucleus. Radioactivity. Nuclear radiations

The atomic nucleus.
Radioactivity. Nuclear radiations
László Smeller
Why?
Medical application of nuclear radiation:
Nuclear imaging
Radiotherapy
Length scale of the nature
10-10 – angstrom diameter of an atom, bond length
H atom ∅ ≈ 1 angstrom (Å)
10-12• picometer wavelength of the X-ray
10-15• femtometer size of the nucleus
ee-
10-10 m
m
100• meter
men
10-3• millimeter letters you can read
10-6• micrometer size of a cell (e.g. erytrocyte)
∅ 7μm
-9
10 • nanometer protein
The electrons and the nucleus
e-
Electrons:
=>chemical properties
e-
eee-
e-
e-
10-15 m
e-
ee-
ee-
ee-
Nucleus:
=> radioactivity
Structure of the nucleus
Stability of the nucleus
Elementary charge=1,6·10-19 C
charge
p
mass
proton
+1 e
1 atomic
mass unit
neutron
0
1 atomic
mass unit
n
A (mass number) = number of protons
+ number of neutrons
Z (atomic number) = number of protons
99
43
Tc
• Coulomb force: destabilization
(electrostatic repulsion between the protons)
• Nuclear force: very strong
attractive force
acts only on short range (~fm)
independent on the charge
• Quantized energy levels for the nucleus.
• Typical binding energy is in the MeV range
eV=1,6·10-19 J
99 nucleon, 43 proton and 56 neutron
Isotopes
Table of isotopes
Number of neutrons is different
Variants of the same element
⇒ the chemical properties are identical.
Pl:
18
F
9
unstable
(radioactive)
19
F
9
stable
20
F
9
Number of protons
Number of protons is the same
unstable
(radioactive)
isotope <-> radioactive isotope
Number of neutrons
E
Number of protons
Number of protons
Number of neutrons
Number of neutrons
α - decay
Radioactive decays and particles
α - decay
α - particle =
β - decay : β-
β- particle =
β+ particle =
β+
4
2
He nucleus
α - decay: an α particle (4He nucleus) will be emitted
typical for the heavy atoms
electron
positron
Isomeric transition
γ-ray
K-electron capture
characteristic x-ray photon
A
Z
e.g.
Line spectrum
Eα ~ MeV
X⎯
⎯→ ZA−−42Y + 24α
226
88
4
Ra ⎯
⎯→ 222
86 Rn + 2 α
Nα
Eα
β−
neutron surplus
A
Z
n
- decay
X⎯
⎯→ Y + β +ν
A
Z +1
p
1
0
0
−1
n→ p + β + ν
1
1
0
−1
p
e-
β−-ray
ν
e.g. :
32
15
F
32
15
P
59
26
Fe
A
Z
n p
Nβ
n
e+
ν
Emax
p
15
8
O
0
+1
18
9
p →01n + +10β + ν
leave the
nucleus
e.g. :
β+-ray
30
15
52
26
n
p
γ
The parent and daughter atoms can be separated:
the daughter atom emits only γ-radiation!
=> Isotope diagnostics (nuclear imaging)
E.g.:
99mTc
99
42
−
β
γ
99 m
99
Mo ⎯⎯→
⎯→
43Tc ⎯
43Tc
66 h
Atomic number, mass number are unchanged.
Fe
continous energy spectrum
If the excited state of the daughter nucleus is metastable,
the γ-radiation will be emitted later.
α or β
F
30
P⎯
⎯→14
Si + +01β + ν
Isomeric transition
E
C
These isotopes must be produced
artificially (e.g. in cyclotron)
Eβ
The daughter nucleus has an energetically
unfavoured arrangement of nucleons.
n
6
X⎯
⎯→ Y + β +ν
A
Z −1
1
1
p
e.g.: 11
- decay
remains in
the nucleus
Prompt γ-radiation
The surplus energy will be
immediately (ns) emitted in
form of the γ radiation
β+
proton surplus
I
0
P⎯
⎯→32
16 S+ −1 β + ν
continous
energy spectrum
β − = −10β = e −
9
131
53
leave the
nucleus
remains in
the nucleus
n
e.g.: 20
6h
K-capture (inverse β-decay)
e-
ee-
e-
e-
e-
p
e-
e-
e-
eee-
1
1
p
n
x-ray
e-
e-
e-
e-
ee-
ee-
e-
n
e-
e-
e-
ee-
Some examples of the decay paths
v
e-
ee-
p + −10β → 01n + ν
Activity (Λ)
Characteristics of radioactive decays
in general
Λ=
activity
characterizes the source
half life time
depends on the type of the isotope
characterizes the speed of the decay
particle energy
characterizes the radiation
dN
dt
⎛ ΔN ⎞
⎟
⎜=
⎝ Δt ⎠
N = Number of
undecayed atoms
t = time
ΔN = Number of decays
during Δt time
Activity= number of decays in a unit time
unit: becquerel Bq
1 Bq= 1 decay/sec
kBq, MBq, GBq, TBq
immeasurably
small
level of natural
activity
in vivo
diagn.
careful
work with
it!
activity applied
in radiotherapy
Law of radioactive decay
Law of radioactive decay
N (t ) = N 0e
ΔN = −λNΔt N: Number of undecayed nuclei
λ decay constant (probability of the decay)
T half life (T1/2)
τ average lifetime
Theoretically never decreases to zero !
No/2
No/e
No/4
N (t ) = N 0 e − λt
Exponential decrease
No/8
0
ΛN
Λo
N (t ) = N 0 e
− λt
− λt
= Λ0 2
−
t
T
Λo/2
Λ decreases on the same mode as N!
Λo/4
Theoretically never decreases to zero!
Λo/e
Λo/8
0
0
T1/2
2T1/2
τ
3T1/2
time
2T1/2
3T1/2
During about 10 T the
activity decreases to its
1/1000 (e.g GBq->MBq)
time
ln 2 0,693
=
T
T
Few examples for half life
232Th
238U
40K
Λ=λN
Λ(t ) = Λ0 e
T1/2
τ
Decrease of the activity as a function
of time
dN
= −λN
dt
λ=
0
number of undecayed atoms at t=0
dN
Λ=
dt
t
T
No
Differential equation
solution:
= N0 2
−
N
λ: decay constant (probability of the decay [1/s])
1/λ=τ average lifetime
dN
= −λN
dt
− λt
14C
137Cs
3H
1,4·1010 y
4,5 ·109 y
1,3 ·109 y
5736 y
30 y
12,3 y
60Co
59Fe
56Cr
131I
99mTc
18F
11C
Don’t learn these numbers!
15O
222Th
5,3 y
1,5 m
1 m (28 d)
8d
6h
110 min
20 min
2 min
2,8 ms
Typical energy levels in the
microworld
Excitation of the
outer electrons
Electron transition
between inner
electrons
Transformation
of the nucleus
(decay)
keV (fJ)
MeV (pJ)
X-ray
Nuclear
radiation
α, β, γ
eV (aJ)
light
Absorption of the nuclear radiation
α
β−
β+
direct
ionization
particles with electric charge
different types of interactions with matter!
γ
(x-ray)
uncharged particles (photons)
indirect
ionization
not a nuclear radiation, but its absorption
is similar to that of the γ radiation
Absorption of the charged particles
Ionizing during the path => continuous decrease of the particle energy
The energy after a given path length decreases to the thermal value
effective range
++
+
+ +
+
++
+
+
++
+ +
+
+
+
β−-particle
α-particle
in air
~m
few cm
~ cm
in tissue 0,01-0,1 mm
+
+
β− + + + +
+ +
+
+
α
Effective range
+
+ +
N
N
effective
range
penetration depth
effective range
penetration depth
+
Applications

Download Report