Transcript +1/2

Chapter 3
Nuclear properties
TOPICS
 Nuclear binding energy
 Radioactivity
 Artificial isotopes
 Nuclear reactions
 Separation of radioactive isotopes
 Applications of isotopes
 Sources of 2H and13C
 Nuclear magnetic resonance spectroscopy:
applications
Mo¨ssbauer spectroscopy: applications
3.2 Nuclear binding energy
Mass defect, and binding energy
• mass defect
- atomic mass of any atom besides 1H is less than the sum of the
protons, neutrons, and electrons.
- is a measure of the binding energy of the protons and neutrons
in the nucleus
-loss of mass and liberation of energy are related by Einstein’s
equations.
DE = Dmc 2
Where DE = energy libarated
Dm = loss of mass
C = speed of light in a vacuum = 2.998 x 108 ms-1
The sum of the masses of the protons, neutrons and electrons in a Li atom
Fig. 3.1 Variation in
average binding energy
per nucleon as
a function of mass
number. Note that the
energy scale is positive,
meaning that the nuclei
with the highest values
of the binding energies
release the greatest
amount of energy upon
formation.
Mev = mega electron vollt
note that the binding energy per nucleon
decreases appreciably for mass numbers > 100.
The average binding energy per nucleon
it is more useful to consider the average binding energy per nucleon, i.e. per particle in
the nucleus.
3.3 Radioactivity
Nuclear emissions
If a nuclide is radioactive , it emits particles or electromagnetic
radiation or undergoes spontaneous fission or electron capture.
An example of spontaneous radioactive decay is that of carbon14, which takes place by loss of a b-particle to give nitrogen-14.
This decay is the basis of radio-carbon dating. The emission of a
b-particle results in an increase in the atomic number by 1 and
leaves the mass number unchanged.
A positron is of equal mass but opposite charge to an electron.
A neutrino and an antineutrino possess near zero masses, are
uncharged and accompany the emission from the nucleus
of a positron and an electron respectively.
Nuclear transformations
The kinetics of radioactive decay
Fig. 3.4 Radioactive decay
follows first order kinetics and
a plot of the number of
nuclides against time is an
exponential decay curve. The
graph shows a decay curve
for radon-222,which has a
half-life of 3.82 days
3.4 Artificial isotopes
Nuclear reactions may occur when nuclei are bombarded with
high energy neutrons or positively charged particles.
Production of artificial nuclides has two consequences:
• production of artificial isotopes of elements that do no not possess naturally occurring
radioisotopes
• synthesis of transuranium elements (Z ≥ 93), nearly all of which are exclusively manmade.
3.5 Nuclear fission
A particular reaction path during nuclear
fission is called a reaction channel
The fission of uranium-235
The general point
that the sum of the
mass numbers of the
two fission products
plus the neutrons
must equal 236.
Since each neutron can initiate another nuclear reaction,
a branching chain reaction is possible. If this involves a quantity of
235U larger than a certain critical mass, a violent explosion occurs,
liberating enormous amounts of energy.
Fig. 3.6 A representation of a branched chain reaction in which each step of the reaction
produces two neutrons, each of which can initiate the fission of a 235U nuclide. If left
uncontrolled, such a chain reaction would lead to a violently explosive situation.
‫اليورانيوم هو المكون الوحيد الذي يمكن أن ينتج طاقة نووية‪ ،‬يحتوي اليورانيوم الطبيعي على ذرات ذات كتالت مختلفة تسمى‬
‫النظائر وتوجد عادة في اليورانيوم ‪ 238‬واليورانيوم ‪ .235‬والنسب كما يلي‪:‬‬
‫النظائر األخرى ‪%0،01 -‬‬
‫(اليورانيوم ‪% 0،7- )235‬‬
‫(اليورانيوم ‪% 99،3 -)238‬‬
‫التخصيب هو عملية فصل اليورانيوم ‪ 238‬واليورانيوم ‪ ،235‬ويتم بواسطة الطرد المركزي للغاز‪ .‬حيث يتم تغذية االسطوانة‬
‫الدائرة (الطرد المركزي) ‪-‬التي تدور على قاعدة يديرها محرك ‪ -‬بغاز اليورانيوم هكسا فلورايد ‪ -‬يذهب اليورانيوم في حالته‬
‫الغازية إلى جهاز الطرد المركزي ويحول من ‪ 70-50‬ألف دورة في الدقيقة‪.‬‬
‫اليورانيوم المخصب‬
‫يستخدم اليورانيوم المخصب في صناعة القنابل النووية‪ ،‬حيث يجب أن يرتفع مستوى اليورانيوم ‪ 235‬قبل أن يتم حرقه كوقود‬
‫في المفاعالت النووية أو استخدامه لصنع األسلحة النووية‪.‬‬
‫األسلحة النووية‬
‫خالل فترة عام يمكن لعدد ‪ 1500‬من أجهزة الطرد المركزي أن تنتج كمية كافية من اليورانيوم عالي التخصيب إلنتاج قنبلة‬
‫نووية واحدة‪ .‬في حالة األسلحة النووية يكون مستوى اليورانيوم ‪ 235‬فوق ‪ %90‬مقارنة بنسبة اليورانيوم ‪ 238‬وبذلك يكون‬
‫اليورانيوم ‪ 235‬قابل لالحتراق‪.‬‬
‫الكتلة الحرجة لبعض المواد‬
‫بعض تلك الكتل الحرجة للكتلة الكروية العارية‪ ،‬أي من دون عاكس للنيوترونات يعمل على رد النيوترونات الخارجة من‬
‫الكتلة لتحفيز تفاعلها مع المادة النووية‪.‬‬
‫كتلة حرجة يورانيوم‪ 52 : 235-‬كيلوجرام‪ ،‬أي كرة قطر ‪ 17‬سم‪،‬‬
‫كتلة حرجة بلوتونيوم‪ 10 : 239-‬كيلوجرام‪ ،‬أي كرة قطر ‪ 10‬سم‪،‬‬
‫كتلة حرجة بلوتونيوم‪ 40 : 240-‬كيلوجرام‪ ،‬أي كرة قطر ‪ 15‬سم‪،‬‬
‫وتعتمد الكتلة الحرجة على درجة نقاوة المادة إذ أن الشوائب تمتص النيوترونات وتمنعها من التفاعل‪ ،‬فمثال إذا كان‬
‫اليورانيوم‪ 235-‬مخصبا بدرجة ‪ % 20‬فقط تصبح الكتلة الحرجة فوق ‪ 400‬كيلوجراما‪ ،‬وإذا كان اليورانيوم مخصبا لدرجة‬
‫‪ % 15‬تصبح الكتلة الحرجة فوق ‪ 600‬كيلوجراما‪ .‬أما الثالثة أرقام المذكورة أعاله فهي لدرجة تخصيب تبلغ ‪.% 99‬‬
Production of energy by nuclear fission
Transuranium elements
Table 3.2 The
transuranium
elements. The
names are those
agreed by the
IUPAC.
3.8 Nuclear fusion
An example is the formation of helium-4 from
deuterium and tritium
Compared with fission reactions, nuclear fusion
has the advantage that large quantities of
radioactive products are not formed. However,
the activation energies for fusion reactions are
very high and, up to the present time, it has been
possible to overcome the barrier only by
supplying the energy from a fission reaction to
drive a fusion reaction. This is the principle
behind the hydrogen or thermonuclear bomb
Fusion reactions
are believed to take
place in the Sun
and start at
temperatures above
107K.
3.9 Applications of isotopes
Infrared Spectroscopy (IR)
When the hydrogen atom in an X-H bond is exchanged for deuterium,
the reduced mass of the pair of bonded atoms changes and shifts the position
of the absorption in the IR spectrum due to the X-H stretching mode.
Shifts of this kind can be used to confirm assignments in IR spectra.
An absorption at 3650 cm-1 in the IR spectrum of a compound X has been assigned
to an O-H stretching mode. To what Wave number is this band expected to shift
upon deuteration? What assumption have you made in the calculation?
Kinetic isotope effects
Isotopic labelling may be used to probe the mechanism of a reaction.
Consider the case where the rate-determining step of a reaction involves
breaking a particular C-H bond.
Labelling the compound with deuterium at that site will mean that a C-D rather
than a C-H bond is broken. The bond dissociation energy of a C-D bond is
higher than that of a C-H bond because the zero point energy is lowered when
the reduced mass, , of a bond is increased, i.e. (C-D) > ( C-H)
the rate-determining step should proceed
more slowly for the deuterated compound.
The zero point energy of a molecule
corresponds to the energy of its lowest
vibrational level (vibrational ground
state).
Radiocarbon dating
Radiocarbon dating is a technique used widely by archaeologists
to date articles composed of organic material (e.g. wood).
The method relies on the fact that one isotope of carbon,14C, is
radioactive (t1/2 = 5730 yr) and decays according to equation
Analytical applications
The use of radioisotopes in analysis includes determinations of
solubilities of sparingly soluble salts and vapour pressures of
rather involatile substances, and investigations of solid solution
formation and adsorption of precipitates.
3.10 Sources of 2H and 13C
Solvents for nuclear magnetic resonance (NMR) spectroscopy,
enriched in deuterium to an extent of 99%, are commercially
available. The separation of deuterium from naturally occurring
hydrogen is achieved electrolytically with the isotope in the form of
D2O.
Carbon-13: chemical enrichment
Nuclear Magnetic Resonance
To be successful in using NMR as an analytical tool, it is necessary to understand the
physical principles on which the methods are based.
The nuclei of many elemental isotopes have a characteristic spin (I).
Some nuclei have integral spins (e.g. I = 1, 2, 3 ....), some have fractional spins (e.g. I =
1/2, 3/2, 5/2 ....), and a few have no spin, I = 0 (e.g. 12C, 16O, 32S, ....).
Isotopes of particular interest and use to organic chemists are 1H, 13C, 19F and 31P, all of
which have I = 1/2.
Spin Properties of Nuclei
Nuclear spin may be related to the nucleon composition of a nucleus in the following
manner:
 Odd mass nuclei (i.e. those having an odd number of nucleons) have
fractional spins. Examples are I = 1/2 ( 1H, 13C, 19F ), I = 3/2 ( 11B )
& I = 5/2 ( 17O ).
 Even mass nuclei composed of odd numbers of protons and neutrons
have integral spins. Examples are I = 1 ( 2H, 14N ).
 Even mass nuclei composed of even numbers of protons and
neutrons have zero spin ( I = 0 ). Examples are 12C, and 16O.
The following features lead to the nmr phenomenon:
1. A spinning charge generates a magnetic
field, as shown by the animation on the right.
The resulting spin-magnet has a magnetic
moment (μ) proportional to the spin.
2. In the presence of an external magnetic
field (B0), two spin states exist, +1/2 and
-1/2.The magnetic moment of the lower
energy +1/2 state is aligned with the external
field, but that of the higher energy -1/2 spin
state is opposed to the external field. Note that
the arrow representing the external field points
North.
3. The difference in energy between the two spin states is dependent on the external
magnetic field strength, and is always very small. The following diagram illustrates that
the two spin states have the same energy when the external field is zero, but diverge as
the field increases. At a field equal to Bx a formula for the energy difference is given
)remember I = 1/2 and μ is the magnetic moment of the nucleus in the field(.
For nmr purposes, this small energy
difference )ΔE( is usually given as
a frequency in units of MHz (106 Hz),
ranging from 20 to 900 Mz, depending
on the magnetic field strength and the
specific nucleus being studied.
4. For spin 1/2 nuclei the energy difference between the two spin states at a given
magnetic field strength will be proportional to their magnetic moments. For the four
common nuclei noted above, the magnetic moments are: 1H μ = 2.7927, 19F μ = 2.6273,
31P μ = 1.1305 & 13C μ = 0.7022. These moments are in nuclear magnetons, which are
5.05078•10-27 JT-1. The following diagram gives the approximate frequencies that
correspond to the spin state energy separations for each of these nuclei in an external
magnetic field of 2.35 T. The formula in the colored box shows the direct correlation of
frequency (energy difference) with magnetic moment (h = Planck's constant =
6.626069•10-34 Js).
Why should the proton nuclei in different compounds
behave differently in the nmr experiment ?
The answer to this question lies with the electron(s)
surrounding the proton in covalent compounds and ions.
Since electrons are charged particles, they move in
response to the external magnetic field (Bo) so as to
generate a secondary field that opposes the much stronger
applied field. This secondary field shields the nucleus from
the applied field, so Bo must be increased in order to
achieve resonance (absorption of rf energy). As illustrated
in the drawing on the right, Bo must be increased to
compensate for the induced shielding field. In the following
diagram, those compounds that give resonance signals at
the higher field side of the diagram (CH4, HCl, HBr and HI)
have proton nuclei that are more shielded than those on
the lower field (left) side of the diagram.
Low
Field
Region
Location of Signals
• More electronegative atoms deshield more and give larger shift values.
• Effect decreases with distance.
• Additional electronegative atoms cause increase in chemical shift.
High
Field
Region