Download 6. Divisibility of atoms: from radioactivity to particle physics

6. Divisibility of atoms: from
radioactivity to particle physics
6.1 Discovery and classification
•Becquerel 1896: Uranium salt on top of wrappedup 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!
Ra  Rn  
226
88
222
86
A
4
2
Z
Element
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.
14
7
N  24 189F 178O  p
Decay chains
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
number of neutrons, N
succession of decays
YF fig 43.8
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
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
4
2
He 49Be126C  01n
• 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
1
0
n B Li He
10
5
7
3
4
2
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
E B  (ZM H  Nmn – Z M)c
A
2
Mass defect = EB/c2
1
MH: mass of neutral hydrogen M H 1 H  1.007825 u
mn: mass of neutron (N: number of neutrons)
A
M mass of neutral atom
Z
and c2 = 931.5 MeV/u
Note: atomic binding energy of electrons neglected
since much smaller than nuclear binding energy
Examples:
2
Deuterium 1 H , 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
EB =28.3 MeV
(relevant for fusion)
“Splitting the atom”
In 1932 Cockcroft and Walton performed the following
experiment in Rutherford’s group, Cavendish lab,
Cambridge:
7
3
Li11p24  24
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.
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
dN
 dt;
• Separation of variables:
N
t
N
dN
   dt ; with N0= N(t=t0)
• Integration: 
N
N
t
0
0
ln( N )  ln( N 0 )  ln(
N
)   (t  t 0 );
N0
• thus N (t )  N 0 exp( t ) where we set t0=0.
Half life T1/2 : time required for N to decrease from
N0 to N0/2:
N (T1/2 )  N 0 exp( T1/2 )  N 0 / 2;
T1/2  (1/  ) ln(1/ 2)  ln(2) /   0.693 / 
dN (t )
 N (t )
Activity (decay rate): 
dt
• 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
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
coulomb per kg
1R = 2.58×10−4 C/kg
absorbed dose D
energy absorption of 1 rad = 0.01 J/kg
tissue per unit mass
dose equivalent
DE = QF x D
QF: Quality Factor
biological
effectiveness
1 rem = 10-2 Sv
e.g. 200keV X-rays: QF=1; alpha-particles: QF=20;
gray 1 Gy = 1J/kg
sievert 1Sv = 1J/kg
x QF
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. n  p    ?

• electrons produced in β-decay have wide energy spectrum;
need third particle that is produced in the decay (Pauli 1931):
anti-neutrino,
 e , electrically neutral, very small rest-mass.
n  p     e
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.
6.6 Short history of discovery of elementary
particle
year
1897
1918
1932
1932
1946
particle
electron
proton
neutron
positron
pion
1946
1955
1956
myon
anti-proton
anti-neutrino
researcher
Thomson
Rutherford
Chadwick
Anderson (predicted by Dirac 1928)
Powell (cosmic rays), predicted by Yukawa
1935
Anderson, Neddermeyer
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
electron-neutrino
muon
tau
(with finite rest-mass)
muon-neutrino tau-neutrino (rest-mass zero?)
all of these also exist as anti-particles
quarks (appear in pairs or triplets):
up
u
2/3
down
d
-1/3
d
strange charm beauty
top
(finite rest-mass)
s
c
b
t
-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   : ud
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!