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

XAZNotation: 29

64 Cu, 47108 Ag, 79

197 Au⏟unique elements

11 H, 1

2 H, 13 H⏟

isotopes

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

227 MeV 494.931kg 10559 660.1u 1 c

Nuclei Sizes

• Scattering experiments determine size

• Measured in femtometers (aka fermis)

• All nuclei have nearly the same density

1.29310 Arr

Fig. 29.2, p. 959

m 10fm 1 15

r0=1.2 fm

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

Fig. 29.4, p. 961

Binding Energy vs. Mass Number

Ai mmm

Radioactivity

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

photonsenergy high :rays

or :particles

nuclei He :particles 42

ee

Fig. 29.5, p. 962

A positron (e+) is the antiparticle of the electron (e−)

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

3.29Nt

NR

Fig. 29.6, p. 919

a4.290teNN

5.29693.02ln

21 T

sdecays 103.7Ci 1 10 sdecay 1Bq 1

Alpha Decay• Unstable nucleus emits

particle (i.e., a helium nucleus) spontaneously

• Mass of parent is greater than mass of daughter plus particle

• Most of KE carried away by particle Fig 29.7, p. 966

29.8HeYX 42

42

AZ

AZ

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

enp

epn10

11

11

10

12.29eYX

11.29eYX

1

1

AZ

AZ

AZ

AZ

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

eCB *126

125

CC 126

126 *

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

00

ln RRteRR t

Natural Radioactivity• Three series of naturally occurring

radioactivity

• 232Th more plentiful than

238U or

235U

• Nuclear power plants use enriched uranium

• Other series artificially produced

Thorium Series

Fig. 29.10, p. 971

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 KEminKEmin=(1+ m

M ) ∣Q∣

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)

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

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

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: rem 1mrad 10010min H

β particles: rem 51.0mrad 3007.1max H

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

rem 1.0mrad 1001min H

rem 6mrad 30020max H