Nuclear physics

Nuclear Physics
Properties of Nuclei
Binding Energy
Radioactivity


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
Notation:

A
Z

X


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 12C ≡ 12 u

1 u = 1.660 559 ×10

−27

kg = 931.494 MeV c

2


Nuclei Sizes
• Scattering experiments
determine size
• Measured in femtometers
(aka fermis)
• All nuclei have nearly the
same density

Fig. 29.2, p. 959

r = r0 A

13

1 fm ≡ 10 −15 m

[ 29.1]


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


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

∆m = ( ∑ mi ) − m A

Binding Energy vs. Mass Number

Fig. 29.4, p. 961


Radioactivity
• Unstable nuclei decay to more stable nuclei
• Can emit 3 types of radiation in the process

α particles : He nuclei
4
2

β particles : e − or e +
γ rays : high energy photons
A positron (e+) is the antiparticle
of the electron (e−)
Fig. 29.5, p. 962


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

1 Ci ≡ 3.7 ×1010 decays s 1 Bq = 1 decay s
∆N
R=
= λN
∆t

[ 29.3]

N = N 0 e − λt

ln 2 0.693
T1 2 =
=
λ
λ

[ 29.5]

[ 29.4a ]
Fig. 29.6, p. 919


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
A
Z

X→

Fig 29.7, p. 966
A− 4
Z −2

Y + He
4
2

[ 29.8]


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

n → p + e +ν

A
Z

X→

p → 01n + e + + ν

A
Z

X → Z −A1Y + e + + ν

1
0
1
1

Fig. 29.8a, p. 968

1
1

−

A
Z +1

Y + e +ν
−

[ 29.11]
[ 29.12]


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
12
5

B → 126C* + e − + ν

12
6

C* → 126C + γ


Radioactive

Carbon Dating
• Cosmic rays create 14C
from 14N
• Constant ratio of 14C/ 12C
(1.3×10–12) in atmosphere
• Living organisms have
same ratio
• Dead organisms do not (no
longer absorb C)
• T½ of 14C = 5730 yr
• Measure decay rates, R

R = R0 e

− λt

ln ( R R0 )
⇒t =−
λ


Natural Radioactivity
• Three series of naturally occurring
radioactivity
•

232

238

Thorium Series

235

Th more plentiful than U or U
• Nuclear power plants use enriched
uranium
• Other series artificially produced
Fig. 29.10, p. 971


Nuclear Reactions
• Accelerators can
• Atomic and mass
generate particle
numbers (Z and A) must
energies up to 1 TeV
remain balanced
• Bombard a nucleus with • Mass difference before
energetic particles
and after reaction
determines Q value
• Nucleus captures the
– Exothermic: Q > 0
particle
– Endothermic: Q < 0
• Result is fission or fusion
• Endothermic requires
incoming particle to have
KEmin

Fusion and Fission


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.)


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)

1 R ≡ amount of
radiation that
Roentgen (R)
Ionization per kg
produces
2.58×10−4 C/kg

Absorbed Dose (D)

1 Gray (Gy)
Energy
absorbed per kg
≡ 1 J/kg

1 rad = 10−2 Gy

Relative Biological
How much more damage is done compared to X or γ
Effectiveness (RBE) rays of equivalent energy (unitless).
Damage
Dose Equivalent (H)
expected

1 Sv
≡ 1 RBE×Gy

1 rem = 10−2 Sv


RBE Factors
Radiation Type
X and γ rays

RBE Factor
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

Sources of Ionizing Radiation

From Touger, Introductory Physics, Table 28-4, p. 817


Typical Dose Equivalents

From Touger, Introductory Physics, Table 28-4, p. 817


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:
β particles:

H min = (10 )(100 mrad ) = 1 rem

H max = ( 20 )( 300 mrad ) = 6 rem

H min = (1)(100 mrad ) = 0.1 rem

H max = (1.7 )( 300 mrad ) = 0.51 rem

α particles are more effective at delivering a dose, but do
not penetrate as far as β particles