6. Divisibility of atoms: from

radioactivity to particle physics

6.1 Discovery and classification

•Becquerel 1896: Uranium salt on top of wrapped-

up photographic plate produces an image

•Marie and Pierre Curie extract Polonium and

Radium from the salt: much more radioactive

•1gram Ra has power of 0.015 Watt

•taking into account half-life of Ra (1500 years),

emits 10000 times more energy than is released by

burning 1g of coal

three different types of radiation:

• negatively charged particles (deflection in magnetic field) (β)

• positively charged particles (deflection in magnetic field, but

much weaker) ()

• radiation, not deflected using electromagnetic fields (γ)

• β-particles identified as electrons by q/m value

• -particles q/m = 4.826x107 C/kg, half as much as hydrogen ion

• Faraday beaker for collection of charges and counting number

of particles: q=2e, thus = 4He2+

• Radioactive decay: change of the type of element, atoms

have no longer the unchangeable character attributed to

them since the early days of Greek philosophy!

atomic number Z reduced by 2 in -decay,

mass number A reduced by 4

: Z→Z-2, A→A-4;

• β-decay: Z→Z+1, A→A;

• Generally: resulting daughter nucleus also unstable,

results in various decay series with end-product around lead.

• 1919 Rutherford: artificial change of an element by

bombarding Nitrogen with -particles. pOFN 17

8

18

9

4

2

14

7

42222

86

226

88 RnRa ElementA

Z

Decay chains

succession of decays

as long as decay is energetically

possible it will occur

rates at which the decays occur

depends on both type of nucleus and

type of decay

inverse of rate is called lifetime of the

nucleus, it equals the half-life (shown in

figure) divided by ln(2)

stable endpoint reached when it is no

longer energetically feasible for nucleus

to undergo either alpha- or beta-decay

YF fig 43.8

nu

mb

er

of

neu

tro

ns, N

number of protons, atomic number Z

6.2 Discovery of the neutron

• why is charge to mass ratio not the same for all nuclides?

(isotopes of the same element, chemically not

distinguishable)

• 1930 Bethe and Becker, bombardment of Beryllium,

Boron and Lithium with -particles: target particle emits

radiation with greater penetration power than -particles

• 1932 Chadwick: new particles electrically neutral, mass

approximately equal to proton: neutrons

nCBeHe 1

0

12

6

9

4

4

2

• Neutrons hard to detect directly (no charge, thus no

ionisation).

• Interaction with nuclei;

they are slowed down (moderated) during scattering;

can penetrate nucleus

• Indirect detection of slow neutrons

HeLiBn 4

2

7

3

10

5

1

0

6.3 Energy and Mass

Definition of atomic mass unit

Recall: 1 mole (SI unit): amount of a substance that

contains as many elementary entities as there are atoms in

12 gram Carbon-12 (12C). The number of entities in a mole of

a substance is given by Avogadro’s number NA.

atomic mass unit u:

1u = 1/12 m(12C) = 1.66053886×10-27kg = 931.494MeV /c2

1g = 6.022142 x 1023 u

Mass defect

proton mass mp = 1.672622×10-27 kg = 1.007276 u

neutron mass mn = 1.674927×10-27 kg = 1.008665 u

electron mass me = 9.10938×10-31 kg = 0.000548580 u

• Nucleus: neutrons and protons,

BUT mass of atoms not simple sum of masses of

its constituents

• Example 12C-atom: m(6p+6n+6e) = 12.0989 u

but by definition: m(C)= 12 u

• Mass defect Δm: when nuclei are formed from nucleons,

energy is released (e.g. γ–rays). Δm = ΔE/c2

Nuclear binding energy

2A

ZnHB)M– Nm (ZM E c

Mass defect = EB/c2

MH: mass of neutral hydrogen

mn: mass of neutron (N: number of neutrons)

mass of neutral atom

and c2 = 931.5 MeV/u

Note: atomic binding energy of electrons neglected

since much smaller than nuclear binding energy

MA

Z

u 1.007825HM 1

1H

Examples:

Deuterium , 1p, 1n, 1 electron; mass: 2.014102 u

EB = (1×1.007825 u + 1×1.008665 u – 2.014102 u) ×

(931.5 MeV / u) = 2.224 MeV

Helium, 2p, 2n: large mass defect (relevant for fusion)

EB =28.3 MeV

H2

1

In 1932 Cockcroft and Walton performed the following

experiment in Rutherford’s group, Cavendish lab,

Cambridge:

They found a release of energy of about 17MeV.

First nuclear confirmation of Einstein’s relationship E=mc2

results in Nobel Prize for Cockcroft and Walton in 1951.

4

2

4

2

1

1

7

3 pLi

“Splitting the atom”

Ernest Thomas Sinton Walton 1903-1995

• TCD

1922-26 undergraduate in maths and science

1926-27 MSc (hydrodynamics)

• Cambridge 1927-34, PhD 1931

• TCD Physics Department 1934 – 1974

Erasmus Smith Professor of Natural and

Experimental Philosophy and Head of Physics

6.4 Law of radioactive decay

• Number N of decaying atoms (N large)

• rate of decay (activity) proportional to N:

-dN(t)/dt = λ N(t); λ, decay constant

• Separation of variables:

• Integration: with N0= N(t=t0)

• thus where we set t0=0.

;dtN

dN

;

00

t

t

N

N

dtN

dN

);()ln()ln()ln( 0

0

0 ttN

NNN

)exp()( 0 tNtN

Half life T1/2 : time required for N to decrease from

N0 to N0/2:

Activity (decay rate):

• 1 decay per second = 1 becquerel = 1 Bq (SI unit)

• 1 curie = 1 Ci = 3.70 x 1010 Bq

applet http://www.walter-fendt.de/ph14e/lawdecay.htm

;2/)Texp() T( 01/201/2 NNN

/693.0/)2ln()2/1ln()/1(T1/2

)()(

tNdt

tdN

Quantifying radiation

measure of old unit SI unit

activity decay rate curie

1Ci=3.7 ×1010 Bq

becquerel Bq

[unit s-1]

exposure ionisation in air roentgen

1R = 2.58×10−4 C/kg

coulomb per kg

absorbed dose D energy absorption of

tissue per unit mass

1 rad = 0.01 J/kg gray 1 Gy = 1J/kg

dose equivalent

DE = QF x D

QF: Quality Factor

biological

effectiveness

1 rem = 10-2 Sv sievert 1Sv = 1J/kg

x QF

e.g. 200keV X-rays: QF=1; alpha-particles: QF=20;

6.5 β-decay

• Origin of electrons in β-decay? If inside nucleus, should have

energies of about 20MeV (Heisenberg’s Uncertainty

Principle). Experimentally: less than 1MeV.

• β-decay: decay of neutron in the nucleus.

• electrons produced in β-decay have wide energy spectrum;

need third particle that is produced in the decay (Pauli 1931):

anti-neutrino, , electrically neutral, very small rest-mass.

N→N-1, M→M, Z→Z+1;

• Anderson,1932, cosmic rays: “positively charged electron”,

opposite charge and different magnetic (spin) properties.

• Soon many other elementary particles were discovered.

? pn

eepn

6.6 Short history of discovery of elementary

particle

year particle researcher

1897 electron Thomson

1918 proton Rutherford

1932 neutron Chadwick

1932 positron Anderson (predicted by Dirac 1928)

1946 pion Powell (cosmic rays), predicted by Yukawa 1935

1946 myon Anderson, Neddermeyer

1955 anti-proton

1956 anti-neutrino Cowan and Reines, (predicted by Pauli and Fermi, 1931)

kaon

hyperons

resonance particles

…

a particle zoo!

6.7 Classification: the standard model (1970-1973)

leptons

electron muon tau (with finite rest-mass)

electron-neutrino muon-neutrino tau-neutrino (rest-mass zero?)

all of these also exist as anti-particles

quarks (appear in pairs or triplets): up down strange charm beauty top (finite rest-mass)

u d s c b t

2/3 -1/3 -1/3 2/3 -1/3 2/3 non-integer electric charges

quarks also carry “colour charge”: red, blue, green

(quantum-chromodynamics)

all of these also exist as anti-particles

three quarks make up baryons, uud = proton; udd = neutron

two quarks make up mesons, such as pion

d

du:

Leptons and quarks are fermions, wave-function describing a pair of identical

particles is anti-symmetric with respect to particle exchange.

Particles with symmetric wave-function with respect to particle exchange:

bosons.

forces between particles are transmitted via bosonic field quanta

Force field quantum

Gravitation graviton (not yet discovered)

Weak force (governing beta decay) W+,W-, Z0

Strong nuclear force (between quarks) 8 gluons (different colour combinations)

Electromagnetic force photons

Further required particle: Higgs bosons (to explain mass difference of

photons (zero mass) and W+,W-, Z0)

Fundamental Forces

• A Theory Of Everything (TOE) would unify the

theories for the four different fundamental forces. (But

it would not mean the end of physics!)

• Electro-magnetic and weak nuclear force have been

unified: electro-weak theory. Theories unifying

electro-weak theory with the strong nuclear force are

called Grand Unified Theories (GUT). Problem:

incorporation of gravity; attempted by string

theories(10 or 26 dimensions)

ongoing problem!

Figure for standard model: http://en.wikipedia.org/wiki/Image:Particle_chart.jpg

Large Hadron Collider at CERN (see Physics World, March 2011, p21-30)

• particle accelerator with circumference 27km, 100m

underground; four experimental caverns

• Since 2008 study of proton-proton collisions, energies

7TeV, eventually 14TeV

Investigating the standard model

• are quarks and leptons really point particles?

(experiments: d< 50 x 10-21 m)

• Higgs particle is required to account for finite mass of

W+,W-,Z bosons; Dec. 2011: “tantalising hints” of new

particle (mass about 125 GeV); 2013: Nobel prize for

Higgs and Englert

• Gravity is not included in standard model

• Alternative theories exist:

SUperSYmmetry theory predicts further particles (additional

generations), detectable at higher energies?

Large Extra Dimension theory, to explain weakness of

gravity

String theory: still does not seem to provide experimentally

testable predictions

September 2011: “faster than

light” neutrinos?

(which would falsify relativity theory!)

February 2012: Dodgy optical fibre cables?

Muon-neutrinos produced in CERN, detected at OPERA

detector, Gran Sasso, Italy (730km apart), did they arrive

60.7 nanoseconds too early?

June 2012: not faster than speed

of light (there were indeed measurement errors!)

Interesting times for physicists!