# Nuclear Magnetic Resonance NMR (PowerPoint)

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```							     and  decays, Radiation
Therapies and Diagnostic,
Fusion and Fission

diagnostic

Evaluations for Prof. T. Montaruli today
Previous lecture: nuclear physics
Final Exam
• Fri, Dec 21, at 7:45-9:45 am in Ch 2103
• About 40% on new material
• 2 sheets allowed (HAND WRITTEN!)

• The rest on previous materials covered by
MTE1 MTE2 MTE3.
New material not covered by
MTE1,2,3
• Ch 40.4-5 particle in a box: wave functions, energy levels,
photon absorption and emission, 40.10 tunneling
• Ch 41.1-3 H-atom quantum numbers and their meaning,
wave functions and probabilities, electron spin
• Ch 41.4-6 Pauli exclusion principle, multi-electron atoms,
periodic table, emission and absorption spectra
• Ch 41.8 Stimulated emission and Lasers
• Ch 42.1-3 Nuclear structure, atomic mass, isotopes,
binding energy, the strong force
• Ch 42.5 Radioactivity, Ch 42.6 Nuclear decay, Ch 42.7
Biological applications
Women Nobel Prizes
The only 2 female Nobel Prizes in Nuclear
Physics!
1903 Marie Curie (with Pierre)
in recognition of the extraordinary services they
have rendered by their joint researches on the
Henri Becquerel

Maria Goeppert-Mayer
1963 Shell Model of Nucleus
Nuclear Physics
• Strong force: attractive force keeping p and n in nucleus (short
range)
• It is convenient to use atomic mass units to express masses
– 1 u = 1.660 539 x 10-27 kg
– mass of one atom of 12C = 12 u
12
• Mass can also be expressed in MeV/c2
– From rest energy of a particle ER = mc2                   6
C
– 1 u = 931.494 MeV/c2

• Binding energy: mnucleus < Zmp + (A-Z)mn = Zmp + Nmn
• The energy you would need to supply to disassemble the nucleus
into nucleons Ebinding = (Zmp+Nmn-mnucleus)c2 = (Zmp+Zme+Nmn+
-Zme-mnucleus)c2 =(ZmH + Nmn - matom) c2              5
Fission and Fusion

6
Stable and Unstable Isotopes

Isotope = same Z
Isotone = same N
Isobar = same A
Stability of nuclei
• Dots: naturally occurring isotopes.
created in the laboratory.
• Light nuclei are most stable if N=Z
• Heavy nuclei are most stable if
N>Z
• As # of p increases more neutrons
are needed to keep nucleus stable
• No nuclei are stable for Z>83
• Discovered by Becquerel in 1896
• spontaneous emission of radiation as result of
decay or disintegration of unstable nuclei
• Unstable nuclei can decay by emitting some
form of energy
• Three different types of decay observed:
Alpha decay  emission of 4He nuclei (2p+2n)
Beta decay electrons and its anti-particle (positron)
Gamma decay high energy photons

• Alpha radiation barely penetrate a piece of
paper (but dangerous!)
• Beta radiation can penetrate a few mm of Al
• Gamma radiation can penetrate several cm of

The Decay Rate
• probability that a nucleus decays during Δt
Prob(in t)  rt
Constant of proportionality r = decay rate (in s-1)

• number of decays (decrease)= NxProb=rNΔt

N=number of independent nuclei
rt
N                             N(t)  N 0e
 rN
t
nuclei at time t               at t=0
The number of decays per second is the activity

N                  1
R     rN                 time constant
t                  r
The half-life
• After some amount of time, half the radioactive
nuclei will have decayed, and activity
decreases by a factor of two.
• This time is the half-life        N0
N(t1/ 2 )      N 0ert1/ 2
2

ln 2
 t1/ 2        ln 2  0.693
         r
Units
• The unit of activity, R, is the curie (Ci)
–
• The SI unit of activity is the becquerel (Bq)
–
• Therefore, 1 Ci = 3.7 x 1010 Bq
• The most commonly used units of activity are
the millicurie and the microcurie
An Example
N0
N(t1/ 2 )      N 0ert1/ 2
•   232Th has a half-life                           2
N0
of 14 x109 yr
• Sample initially
contains: N0 = 106        
232Th atoms
N0/2
N0/4
• Every 14 billion
N0/8
years, the number
of 232Th nuclei goes
down by a factor of
two.
•   14C
(Z=6) has a half-life of 5,730 years, continually
decaying back into 14N (Z=7).
• In atmosphere very small amount! 1 nucleus of 14C each
1012 nuclei of 12C

If material alive,               After death, no exchange
atmospheric                      with atmosphere. Ratio
carbon mix                       changes as 14C decays
ingested (as CO2),
ratio stays
constant.

So can determine time since the plant or animal died
(stopped exchanging 14C with the atmosphere) if not
older than 60000 yr
Carbon dating

A fossil bone is found to contain 1/8 as much
14C as the bone of a living animal. Using

T1/2=5,730 yrs, what is the approximate age
of the fossil?

A. 7,640 yrs
Factor of 8 reduction in 14C
B. 17,190 yrs      corresponds to three half-lives.
C. 22,900 yrs      So age is 5,730 x 3 =17,190 yrs
D. 45,840 yrs
Decay processes:  = 4He
Heavy nucleus spontaneously
emits alpha particle

• nucleus loses 2 neutrons and 2 protons.
• It becomes a different element (Z is changed)
• Example:                                   Alpha particle
238
92 U  He 4
2
234
90 Th
92 protons                    90 protons
2 protons
146 neutrons                  144 neutrons
2 neutrons
A quantum process
• This is a quantum-mechanical process
– It has some probability for occurring.
• For every second of time, there is a probability
that the nucleus will decay by emitting an -
particle.
• This probability depends on the width of the
barrier
Coulomb repulsion
• The  -particle quantum-mechanicallydominates out
tunnels
of the nucleus even if
energy is not > energy barrier

Nuclear attraction dominates   Potential energy of in
the daughter nucleus vs
distance
Disintegration Energy
• In decays energy-momentum must be conserved
• The disintegration energy appears in the form of kinetic energy
of products

MXc2 = MYc2 + KY + Mc2 + KEKY K= (Mx – My – M)c2

Textbook: neglect KY since
M<<MY E=K~ (Mx – My – M)c2

• It is sometimes referred to as the Q
value of the nuclear decay
Number of protons   Decay sequence of         238U

 decay

Number of neutrons
Q ui Ti e™ anda
TI FF( U ededpr esed) t hi opi ur e. r
ar e ncom t s se decm pr esso
n
e
ckm
o e      s c t                 Zone 1 Highest Potential (greater than 4 pCi/L)
• Radon is in the   238U   decay            Q ui Ti e™ anda
TI FF( U ededpr esed) t hi opi ur e. r
ar e ncom t s se decm pr esso
n
e
ckm
o e      s c t
Zone 2 Moderate Potential (from 2 to 4 pCi/L)
series
• Radon is an  emitter that
presents an environmental
hazard
• Inhalation of radon and its
daughters can ionize lung                                Q ui Ti e™ anda
TI FF( U ededpr esed) t hi opi ur e. r
ar e ncom t s se decm pr esso
e
n
ckm
o e      s c t

cells increasing risk of lung
cancer                                                                                              QuickTime™ and a
TIFF (Uncompressed) decompressor
are neede d to see this picture.
• Madison is in Zone 1!
• In USA 20000 people die but
a Geiger can help to identify
problem in houses
• Also used to predict
Earthquakes!

• 222Rn has a half-life of 3.83 days.
• Suppose your basement has 4.0 x 108
such nuclei in the air. What is the activity?
We are trying to find number of decays/sec.
So we have to know decay constant to get R=rN

0.693             0.693
r                                    2.09 106 s
t1/ 2   3.83days  86,400s /day
dN
R       rN  2.09 106 s  4.0 108 nuclei  836decays/s
dt
1Ci
R  836 decays/s                       0.023Ci
2.7 10 decays/s
10
The degree and type of damage caused by radiation depend on
• Type and energy of the radiation
• Properties of the absorbing matter
Radiation damage in biological organisms is primarily due to
ionization effects in cells that disrupts their normal functioning

Alpha particles cause extensive damage, but penetrate only to a
shallow depth
Gamma rays can cause severe damage, but often pass through
the material without interaction
Other kind of radiations: eg. neutrons penetrate deeper and
cause more damage.
QuickTime™ and a
TIFF (Uncompressed) decompre ssor
are neede d to see this picture.

The British authorities said today that A. V. Litvinenko, a former Russian Federal Security Service
liutenant-colonel, and later dissident, died of radiation poisoning due to a rare   and highly
radioactive isotope known as Polonium 210.
Highly radioactive metalloid discovered by M. Curie

A NIsotopic                   T1/2 Activity                                         QuickTime™ an d a
TIFF (Uncompressed) decompressor
are need ed to see this picture.

mass (u)                  (d) (uCi)
210Po 84 126 209.98                    140 0.1

Produced by bombarding bismuth-209 with neutrons in nuclear reactors.         In
the decay 210P creates 140 W/g so 1/2 a gram reaches 500 °C. Considered to
power spacecrafts.
Used in many daily applications: eg anti-static brushes in photographic shops
Dangerous only if ingested because it is an  emitter.
the energy of 1 kg of absorbing            produces the same biological damage as
material by 1 x 10-2 J                     1 rad of the radiation being used
rem (radiation equivalent in man) =
dose in rem = dose in rad x RBE

Ground     0.30 rem/yr
Upper limit
Mercury 9 60.6 rem/yr                                                        suggested by US
QuickTime™ an d a
TIFF (Uncompressed) decompressor
gov
Apollo 14 146.2 rem/yr                  are need ed to see this p icture .

0.50 rem/yr
MIR Station 34.9 rem/yr

Space Station 36.5 rem/yr
Beta decay
• Nucleus emits an electron or a positron
• Must be balanced by a positive or negative
charge appearing in the nucleus.

A
Z   X Y  e
A
Z 1
A        A       
Z   X Y'e
Z 1
This occurs as a n
changing into a p or
a p into a n
Example of -decay
•    (radioactive form of carbon) decays by -
14C

decay (electron emission).
• Carbon Z = 6, 14C has (14-6)=8 neutrons.
• A new element with Z = 7
14
6    C 14 N e
7

Beta decay
decreases number of neutrons in nucleus by one
increases number of protons in nucleus by one

We do not see it, but to explain this decay an anti-
neutrino is needed
The Positron and Antimatter
• Every particle now known to have an antiparticle.
• Our Universe seems to contain more matter (we are lucky otherwise
everything would annihilate into photons!)

Quic kTime™ and a
TIFF (Uncompres sed) dec ompress or
are needed to s ee this pic ture.

Positron 1st detection in cosmic
rays through bending in a B-
field and a bubble chamber
(Anderson 1932)
Decay Quick Question
20Na decays in to 20Ne, a particle is emitted? What
particle is it?
Na atomic number Z = 11
Ne Z = 10

20Na has 11 protons, 9 neutrons
A.   Alpha               20Ne has 10 protons, 10 neutrons
B.   Electron beta       So one a proton (+ charge ) changed to a
C.   Positron beta       neutron (0 charge) in this decay.
A positive particle had to be emitted.
D.   Gamma

p  n  e   e
Nuclear Medicine: diagnostic
• Basic Idea:
– Inject patient with radioactive isotope (tracer) that decays
in a positron
– Positrons annihilate with electrons into gamma rays
– Reconstruct the 3-D image

Positron Emission Tomography
image showing a tumor
Positron Emission Tomography -
PET
Gamma Photon #1   Nucleus
(protons+neutrons)
Basic Idea:
tracer isotope emits a positron

e+-e-                                      – Positron collides with a
nearby electron and
annihilates
electrons             – e+ + e-  2
Gamma Photon #2                                          • Two 511 keV gamma rays are
produced
Isotope     Max. Positron Range (mm) • They fly in opposite directions
(to conserve momentum)
18F         2.6
11C         3.8
68Ga        9.0
82Rb        16.5
Emission Detection
Ring of detectors

• If detectors receive gamma rays at the approx. same time, we
have a detection
• Nuclear physics sensor and electronics
Image Reconstruction

• Each coincidence event represents a line in space connecting the two
detectors along which the positron emission occurred.
• Coincidence events can be grouped into projections images, called
sinograms.
• Sinograms are combined to form 3D images
• 50-60% of cancer patients treated with radiation
• Radiation destroys the cancer cells' ability to reproduce and the body
naturally gets rid of these cells.
• Although radiation damages both cancer cells and normal cells, most
normal cells can recover from the effects of radiation and function properly.
• Ionization (stripping atomic electrons) makes nuclear radiation dangerous
• X and -rays (60Co) from 20 KV to 25 MV
• Pion Therapy under study, less
invasive then photons
QuickTime™ an d a
• Neutrons,protons,..                             TIFF (Uncompressed) decompressor
are need ed to see this p icture .
Gamma decay
• Both  and-decays can leave the nucleus in excited state
• The nucleus can decay to a lower energy state (eg the ground
state) by emitting a high energy photon (1 MeV-1 GeV)
The X* indicates a nucleus in an
excited state
Decay Question?
Which of the following decays is NOT allowed?

238 = 234 + 4
1        238
92   U Th  
234
90       92 = 90 + 2

214 = 210 + 4
214        210   4
2         84   Po Pb He
82   2   84 = 82 + 2
14 = 14+0
3   14
C N  
14
          6          7             6 < 7+0




```
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