2. Nuclear Components
• Nucleus contains nucleons: protons and neutrons
• Atomic number Z = number of protons
• Neutron number N = number of neutrons
• Mass number A = number of nucleons = Z + N
• Each element has unique Z value
• Isotopes of element have same Z, but different N and A values
XA
Z
Notation: 29
64
Cu, 47
108
Ag, 79
197
Au⏟
unique elements
1
1
H, 1
2
H, 1
3
H⏟
isotopes
3. Nucleus Charge and Mass
Particle Charge Mass (kg) Mass (u) Mass (MeV/c2
)
Proton +e 1.672 6 E−27 1.007 276 938.28
Neutron 0 1.675 0 E−27 1.008 665 939.57
Electron −e 9.109 E−31 5.486 E−4 0.511
• Unified mass unit, u, defined using Carbon 12
• Mass of 1 atom of 12
C ≡ 12 u
227
MeV494.931kg10559660.1u1 c=×= −
4. Nuclei Sizes
• Measured in femtometers (aka fermis)
• All nuclei have nearly the same density
• Scattering experiments determine size
[ ]1.2931
0 Arr =
Fig. 29.2, p. 959
m10fm1 15−
≡
r0=1.2 fm
5. Nuclear Stability
• An attractive nuclear force must
balance the repulsive electric force
• Called the strong nuclear force
• Neutrons and protons affected by
the strong nuclear force
• 260 stable nuclei
• If Z > 83, not stable
Fig. 29.3, p. 960
6. Binding Energy
• Total energy of nucleus is less
than combined energy of
individual nucleons
• Difference is called the binding
energy (aka mass defect)
• Energy required to separate
nucleus into its constituents
Fig. 29.4, p. 961
Binding Energy vs. Mass Number
( ) Ai mmm −=∆ ∑
7. Radioactivity
• Unstable nuclei decay to more stable nuclei
• Can emit 3 types of radiation in the process
photonsenergyhigh:rays
or:particles
nucleiHe:particles 4
2
γ
β
α
+−
ee
Fig. 29.5, p. 962
A positron (e+
) is the antiparticle of
the electron (e−
)
8. Decay Constant and Half-Life
• Decay rate (aka activity) is number of decays per
second
• λ is the decay constant
• Unit is Curie (Ci) or Becquerel (Bq)
• Decay is exponential
• Half-life is time it takes for half of the sample to decay
[ ]3.29N
t
N
R λ=
∆
∆
=
Fig. 29.6, p. 919
[ ]a4.290
t
eNN λ−
=
[ ]5.29
693.02ln
21
λλ
==T
sdecays103.7Ci1 10
×≡ sdecay1Bq1 =
9. Alpha Decay
• Unstable nucleus emits α particle (i.e., a
helium nucleus) spontaneously
• Mass of parent is greater than mass of
daughter plus α particle
• Most of KE carried away by α particle
Fig 29.7, p. 966
[ ]29.8HeYX 4
2
4
2 +→ −
−
A
Z
A
Z
10. Beta Decay
• Involves conversion of proton to neutron or
vice-versa
• Involves the weak nuclear force
• KE carried away by electron/antineutrino or
positron/neutrino pair
• Neutrinos: q = 0, m < 1 eV/c2
, spin ½, very weak
interaction with matter
Fig. 29.8a, p. 968
ν
ν
++→
++→
+
−
enp
epn
1
0
1
1
1
1
1
0 [ ]
[ ]12.29eYX
11.29eYX
1
1
ν
ν
++→
++→
+
−
−
+
A
Z
A
Z
A
Z
A
Z
11. Gamma (γ) Decay
• Following radioactive decay, nucleus may be left in an excited state
• Undergoes nuclear de-excitation: protons/neutrons move to lower energy
level
• Nucleus emits high energy photons (γ rays)
• No change in A or Z results
ν++→ −
eCB *12
6
12
5 γ+→ CC 12
6
12
6 *
12. Radioactive
Carbon Dating
• Cosmic rays create
14
C from
14
N
• Constant ratio of
14
C/
12
C (1.3×10
–12
) in
atmosphere
• Living organisms have same ratio
• Dead organisms do not (no longer
absorb C)
• T½ of
14
C = 5730 yr
• Measure decay rates, R
( )
λ
λ 0
0
ln RR
teRR t
−=⇒= −
13. Natural Radioactivity
• Three series of naturally occurring radioactivity
•
232
Th more plentiful than
238
U or
235
U
• Nuclear power plants use enriched uranium
• Other series artificially produced
Thorium Series
Fig. 29.10, p. 971
14. Nuclear Reactions
• Accelerators can generate particle
energies up to 1 TeV
• Bombard a nucleus with energetic
particles
• Nucleus captures the particle
• Result is fission or fusion
• Atomic and mass numbers (Z and A)
must remain balanced
• Mass difference before and after
reaction determines Q value
– Exothermic: Q > 0
– Endothermic: Q < 0
• Endothermic requires incoming
particle to have KEmin
KEmin=(1+
m
M )∣Q∣
16. Interaction of Radiation with Matter
• Radioactive emissions can ionize atoms
• Problems occur when these ions (e.g., OH−
, H+
) react chemically with other
ions
• Genetic damage affects reproductive cells
• Somatic damage affects other cells (lesions, cataracts, cancer, fibrosis, etc.)
17. Quantifying Radioactivity
Quantity Definition SI unit Common Unit
Activity
# nuclei that
decay per sec
1 Bq ≡ 1 decay/s 1 Ci = 3.70×1010
Bq
Exposure (defined
for X and γ rays
only)
Ionization per kg
1 R ≡ amount of
radiation that
produces
2.58×10−4
C/kg
Roentgen (R)
Absorbed Dose (D)
Energy
absorbed per kg
1 Gray (Gy)
≡ 1 J/kg
1 rad = 10−2
Gy
Relative Biological
Effectiveness (RBE)
How much more damage is done compared to X or γ
rays of equivalent energy (unitless).
Dose Equivalent (H)
Damage
expected
1 Sv
≡ 1 RBE×Gy
1 rem = 10−2
Sv
18. RBE Factors
Radiation Type RBE Factor
X and γ rays 1.0
β particles 1.0−1.7
α particles 10−20
Slow n 4−5
Fast n and p 10
Heavy ions 20
Table 29.3, p. 974
19. Sources of Ionizing Radiation
From Touger, Introductory Physics, Table 28-4, p. 817
21. Exercise
• Is the dose equivalent greater if you are exposed
to a 100 mrad dose of α particles or a 300 mrad
dose of β particles?
α particles:
( )( ) rem1mrad10010min ==H
β particles:
( )( ) rem51.0mrad3007.1max ==H
α particles are more effective at delivering a dose, but do
not penetrate as far as β particles
( )( ) rem1.0mrad1001min ==H
( )( ) rem6mrad30020max ==H
