```Chapter 2. Radiation
1)
2)
3)
4)
5)
6)
Overview
Decay Dynamics
1) Overview
are the basis of many of the ideas and techniques of atomic
and nuclear physics.
40K
222Rn
is responsible for
higher levels of
many parts of the world.
The uranium decay series.
because it is a gas and
can easily seep out of
the earth into unfinished
basements and then into
the house
1) Overview
transmutations of nuclides
Radioactivity means the emission of alpha ()
particles, beta () particles, or gamma photons ()
etc. from atomic nuclei. The term radioactivity was
actually coined by Marie Curie
Radioactive decay is a process by which the
nuclei of a nuclide emit ,  or  rays etc.
In the radioactive process, the nuclide undergoes
a transmutation, converting to another nuclide.
5
Conservation of charge
Conservation of the number of nucleons A
Conservation of mass/energy (total energy)
Conservation of linear momentum
Conservation of angular momentum
Apparatus similar to that used by Henri Becquerel to determine the magnetic
deflection of radioactive decay products. The magnetic field is perpendicular to the
direction of motion of the decay products.
The law of conservation of mass and energy covers all reactions.
Sum of mass before reaction = Sum of mass after reaction + Q
Q = Sum of mass before reaction - Sum of mass after reaction
Interesting Items:
Before decay
Spectrum（能谱） of particles
Energy in gamma decay
Energy in beta decay
Energy in alpha decay


Recoiling nucleus
a)
Gamma Decay Energy
Gamma, , rays are electromagnetic radiation emitted from atomic nuclei.
The bundles of energy emitted are called photons.
Excited nuclei are called
isomers, and de-excitation is
called isomeric transition (IT).
Energy for photons
hv=Ei-Ef
Ei ____________
hv
Ef ____________
Eothers _________
Nature of Gamma Transitions
Types of Isomeric Transitions and their Ranges of Half-life
J

Partial half life t (s)
Electric dipole
Magnetic dipole
Electric octupole
Magnetic octupole
Electric 24-pole
Magnetic 24-pole
1
1
2
2
3
3
4
4
Yes
No
No
Yes
Yes
No
No
Yes
5.7e-15 E–3 A–2/3
2.2e-14 E–3
6.7e-9 E–5 A–4/3
2.6e-8 E–5 A–2/3
1.2e-2 E–7 A–2
4.9e-2 E–7 A–4/3
3.4e4 E–9 A–8/3
1.3e5 E–9 A–2
E1
M1
E2
M2
E3
M3
E4
M4
Gamma Decay Energy and Spectrum
Gamma transition of 7Li
Various Gamma Transitions in 7Li
&frac12;+ 6.54 MeV
M3
E3
M1
E1
M2
7/2+
4.64 MeV
&frac12; – 0.778 MeV
3/2– ground state
Eγ is the energy of the gamma photon, E* is
the excitation energy (above the ground
state) of the initial parent nucleus, and Ep is
the recoil kinetic energy of the resulting
ground-state nuclide.
a)
Gamma Ray Spectrum of O18
=Q
2h+
Intensity
3.27 MeV
1.98 MeV
1.98
2+
0+
3.27 MeV
5.25 MeV
E
the kinetic energy of the recoil
nucleus is negligible
Intensities of the peaks are related to the
population of the excited state as well as
the half life of the transition.
b)
How is alpha energy evaluated and determined?
What is a typical alpha spectrum
An Ideal Alpha Spectrum
and why?
No.
of

 MeV
8
10
211Po
 particle energy:
|
98.9% 10.02 MeV |
0.5% 9.45
0.5% 8.55
Expeimentally?
207Pb |
7/ +
2
5/ +
2
1/ +
2




|
|
|
 – 0.5%
0.57 MeV  – 0.5%
15
 – 98.9%
0.90 MeV
What is the initial kinetic energy of the alpha
particle produced in the radioactive decay:
The Qα value in mass units
c) Beta Decay Spectra and Neutrino
A Beta Decay Scheme
P D
Z
Z+1
A Typical Beta Spectrum
+  +v
–
Intensity
or # of 
?
E max
Energy of 
Pauli: Neutrino with spin 1/2 is emitted simultaneously with beta, carrying
the missing energy.
17
c)
The mass of the neutrino is negligibly small.
d) Positron Decay Energy
Positron Emission
–
+

19
1)
2)
3)
4)
5)
6)
Overview
Decay Dynamics
137mBa
decay data,
activity or decay rate A decay constant 
Radioactivity or decay rate A is the rate of disintegration of
nuclei. Initially (at t = 0), we have No nuclei, and at time t, we
have N nuclei. This rate is proportional to N, and the
proportional constant is called decay constant .
the number of decays or
transmutations per unit of time
dN
A = – ––––– =  N
dt
ln N = ln No –  t
Integration gives
Also A = Ao e –  t
or
Stochastic process
N = No e –  t
specific activity
normalized to the mass or volume of the sample
Many safety limits and regulations are based on
the specific activity concept
Variation of N as a function of time t
No
N
N = No e
Also A = Ao e
- t
- t
t
nuclei decrease
exponentially with time
as indicated by the
graph here.
As a result, the
same manner.
Note
 N =A
 No = Ao
24
Half-life and its measurement
Condition?
Very long?
Variation of N as a function of time t
Ln(N or A)
No
N
N = No e Also A = Ao e -
ln N1 – ln N2
 = –––––––––––
t1 – t2
t
t
t
t&frac12; *  = ln 2
Be able to apply these
equations!
N = No e– t
A = Ao e – t
Half life is not affected by chemical
and physical state of matter.
t
ln N = ln No –  t
ln A = ln Ao –  t
Determine half life,
25 t&frac12;
Decay Probability for a Finite Time Interval
does not decay
does decay
As the time interval becomes very small, i.e., t —&gt;Δt &laquo; 1,
p(t)dt, probability a radionuclide, which exists at time t = 0, decays in the time
interval between t and t + dt
the probability distribution function for
decay probability distribution
Decay by competing Processes
Ln A
t
λ is the overall decay constant
The probability fi that the nuclide will decay by the ith
mode is
&lt;-How to calculate
What is the probability 64Cu decays by positron
Emission?
The decay constants for the three decay modes of this
radioisotope are λ β+ = 0.009497 h-1, λ β- = 0.02129 h-1, and λ EC =
0.02380 h-1.
The overall decay constant is
The probability that an atom of 64Cu eventually
decays by positron emission is
1)
2)
3)
4)
5)
6)
Overview
Decay Dynamics decay transients
a) Decay with Production
Q(t) is the rate at which the
created
the special case that Q(t) = Q0
(a constant production rate)
N(t) -&gt; Ne = Q0/λ
means?
t -&gt;
the equilibrium condition
Example How long after a sample is placed in a reactor is it
before the sample activity reaches 75% of the maximum
activity?
Assume the production of a single radionuclide species at a
constant rate of Q0 s-1 and that there initially are no
A(t) = Qo[1-exp(-λt)]
0.75Qo = Qo[1-exp(-λt)]
A(0)=0
Amax = Q0
b) Three Component Decay Chains
Daughter Decays Faster than the Parent
λI &lt; λ2,
transient equilibrium: daughter's decay rate is limited
by the decay rate of the parent.
λI &lt;&lt; λ2,
The activity of the daughter approaches that of the parent. This
extreme case is known as secular equilibrium(久期平衡).
Daughter Decays Slower than the Parent
A2(t)= A2(0)e-λ2t +
A2(t)= A2(0)e-λ2t +
the daughter decays in accordance with its normal decay rate.
1)
2)
3)
4)
5)
6)
Overview
Decay Dynamics
The most prominent of the cosmogenic radionuclides
are tritium 3H and 14C.
14N(n,T)12C
and 16O(n,T)14N
14N(n,p)14C
electron?
12.3 a HTO
5730 a CO2
The solar system was formed about 5 billion years ago. These
radionuclides are seen to all have half-lives greater than the
age of the solar system.
Of these radionuclides, the most significant are 40K and 87Rb
since they are inherently part of our body tissue.
238U92

234Th90
+ 42
234Th90

(t1/2 4.5e9 y)
+ – +  (t1/2 24.1 d)
234Pa91
234Pa91
 234U92 + – + 
234U92
. . . (continue)
Only alpha decay changes the mass number by 4.
There are 4 families of decay series.
4n, 4n+1?, 4n+2, 4n+3,
n being an integer.
thorium (4n), uranium (4n + 2),
and actinium (4n + 3)
(t1/2 6.7 h)
. . .
206Pb82
nuclide with Z &gt; 83 is a member of one of
three long decay chains,
The Decay Path of 4n + 2 or 238U Family
234
230
226
222
218
210
Po
210
206
Pb
206
Tl
206
214
Bi
210
Hg
Po
214
Pb
Bi
214
210
Tl
Pb
At
218
Po
Rn
U
238
234
Pa
234
Th
Th
Ra
 decay
Major route
Minor route
 decay
U
The Decay Paths of the 4n + 1 or 237Np93 Family Series
233
(1.6e5 y)
229
Ac89
Th90
(7300 y; minor path)
225
(10 d)
221
213
209
Bi83
209
Po84

Pb82
209
Fr87

217
At85
 (1 min)
213 83
Bi

Tl
81

U92

2.14 x 106 y,
237
Np93
 (2e6 y)
233
Pa91
225
Ra88
1)
2)
3)
4)
5)
6)
Overview