Chapter 3

Nuclear propertiesTOPICS Nuclear binding energy Radioactivity Artificial isotopes Nuclear reactions Separation of radioactive isotopes Applications of isotopes Sources of 2H and13C Nuclear magnetic resonance spectroscopy: applicationsMo¨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.

E = mc 2

Where E = energy libaratedm = loss of massC = 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

The average binding energy per nucleonit is more useful to consider the average binding energy per nucleon, i.e. per particle in the nucleus.

Mev = mega electron vollt

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.

note that the binding energy per nucleon decreases appreciably for mass numbers > 100.

3.3 Radioactivity

If a nuclide is radioactive , it emits particles or electromagnetic radiation or undergoes spontaneous fission or electron capture.

Nuclear emissions

An example of spontaneous radioactive decay is that of carbon-14, which takes place by loss of a -particle to give nitrogen-14. This decay is the basis of radio-carbon dating. The emission of a -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, areuncharged and accompany the emission from the nucleusof a positron and an electron respectively.

Nuclear transformations

The kinetics of radioactive decayFig. 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 isotopesNuclear 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 man- made.

3.5 Nuclear fission

The fission of uranium-235

A particular reaction path during nuclear fission is called a reaction channel

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.

المواد لبعض الحرجة الكتلةرد على يعمل للنيوترونات عاكس دون من أي العارية، الكروية للكتلة الحرجة الكتل تلك بعض

. النووية المادة مع تفاعلها لتحفيز الكتلة من الخارجة النيوترونات- يورانيوم حرجة قطر 52 : 235كتلة كرة أي سم، 17كيلوجرام،

- بلوتونيوم حرجة قطر 10 : 239كتلة كرة أي سم، 10كيلوجرام،- بلوتونيوم حرجة قطر 40 : 240كتلة كرة أي سم، 15كيلوجرام،

من وتمنعها النيوترونات تمتص الشوائب أن إذ المادة نقاوة درجة على الحرجة الكتلة وتعتمد- اليورانيوم كان إذا فمثال فوق % 20بدرجة مخصبا 235التفاعل، الحرجة الكتلة تصبح 400فقط

لدرجة مخصبا اليورانيوم كان وإذا فوق % 15كيلوجراما، الحرجة الكتلة . 600تصبح أما كيلوجراماتبلغ تخصيب لدرجة فهي أعاله المذكورة أرقام  %.99الثالثة

المخصب اليورانيومصناعة في المخصب اليورانيوم النووية يستخدم اليورانيوم القنابل مستوى يرتفع أن يجب حيث ،

في 235 كوقود حرقه يتم أن النووية قبل .المفاعالت النووية األسلحة لصنع استخدامه أوالنووية األسلحة

لعدد يمكن عام فترة اليورانيوم 1500خالل من كافية كمية تنتج أن المركزي الطرد أجهزة من . اليورانيوم مستوى يكون النووية األسلحة حالة في واحدة نووية قنبلة إلنتاج التخصيب 235عالي

اليورانيوم% 90فوق بنسبة اليورانيوم 238مقارنة يكون .235وبذلك لالحتراق قابل

ذرات على الطبيعي اليورانيوم يحتوي نووية، طاقة ينتج أن يمكن الذي الوحيد المكون هو اليورانيوماليورانيوم في عادة وتوجد النظائر تسمى مختلفة كتالت كما. 235واليورانيوم 238ذات والنسب

يلي:99)- 238اليورانيوم( 0) -235اليورانيوم % ( ،3 األخرى % - ،7 0النظائر 01،%

اليورانيوم فصل عملية هو . 235واليورانيوم 238التخصيب للغاز المركزي الطرد بواسطة ويتم ، - - ( بغاز ( محرك يديرها قاعدة على تدور التي المركزي الطرد الدائرة االسطوانة تغذية يتم حيث

من - ويحول المركزي الطرد جهاز إلى الغازية حالته في اليورانيوم يذهب فلورايد هكسا اليورانيوم50-70. الدقيقة في دورة ألف

Production of energy by nuclear fission

Transuranium elements

Table 3.2 The transuranium elements. The names are thoseagreed 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

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.

Infrared Spectroscopy (IR)

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 effectsIsotopic 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 zero point energy of a molecule corresponds to the energy of its lowest vibrational level (vibrational ground state).

the rate-determining step should proceed more slowly for the deuterated compound.

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 ResonanceTo 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 NucleiNuclear 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.

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).

phenomenon:

                                                                                              

The following features lead to the nmr phenomenon:

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.

High FieldRegion

Low FieldRegion

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.