dr. said m. el-kurdi1 nuclear properties chapter 3

Dr. Said M. El-Kurdi 1

Nuclear properties

Chapter 3


3.1 Introduction

In this chapter we are concerned with nuclear properties and reactions involving the nucleus.

The techniques of nuclear magnetic resonance (NMR) and Mössbauer spectroscopies owe their existence to properties of particular nuclei.

3.2 Nuclear binding energy

Mass defect and binding energy

The mass of an atom of 1H is exactly equal to the sum of the masses of one proton and one electron


However, the atomic mass of any other atom is less than the sum of the masses of the protons, neutrons and electrons present.

mass defect

mass defect is a measure of the binding energy of the protons and neutrons in the nucleus, and the loss in mass and liberation of energy are related by Einstein’s equation 3.1.


This corresponds to 3.79 × 1012J or 3.79 × 109 kJ per mole of nuclei, i.e. a huge amount of energy is liberated when the fundamental particles combine to form a mole of atoms.

The average binding energy per nucleon

per particle in the nucleus.


Nuclear reactions as energy sources. A reaction involving nuclei will be exothermic if:

a heavy nucleus is divided into two nuclei of medium mass

(so-called nuclear fission), or

two light nuclei are combined to give one nucleus of

medium mass (so-called nuclear fusion).


3.3 Radioactivity

Nuclear emissions

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

For the decay of a radioactive nuclide, Rutherford initially recognized three types of emission:

-particles (now known to be helium nuclei,42He2+);

-particles (electrons emitted from the nucleus and having high kinetic energies);

-radiation (high-energy X-rays).


An example of spontaneous radioactive decay is that of carbon-14, which takes place by loss of a -particle to give nitrogen-14

More recent work has shown that the decay of some nuclei involves the emission of three other types of particle:

the positron (+); is of equal mass but opposite charge to an electron.

the neutrino (ve); A neutrino antineutrino possess near zero masses, is

uncharged and accompany the emission from the nucleus of a positron.

the antineutrino. An antineutrino possess near zero masses, is

uncharged and accompany the emission from the nucleus of an

electron.


A comparison of the penetrating powers of -particles, -particles, -radiation and neutrons.


Nuclear transformations

the radioactive decay of uranium-238 to thorium-234. The loss of the -particle is accompanied by emission of -radiation, but the latter affects neither the atomic number nor the mass number.

The -particle in equation is shown as neutral helium gas.

Many nuclear reactions, as opposed to ordinary chemical reactions, change the identity of (transmute) the starting element.


The decay series continues with successive nuclides losing either an - or -particle until ultimately the stable isotope Pb-206 is produced. All steps in the series take place at different rates.


The kinetics of radioactive decay

Radioactive decay of any nuclide follows first order kinetics.

In a first order process, the rate of the reaction:

N, the number of nuclei present

where t = time; k = first order rate constant


A characteristic feature is that the time taken for the number of nuclides present at time t, Nt, to decrease to half their number, Nt/2, is constant. This time period is called the half-life, t1/2, of the nuclide.

radioactive decay is temperature-independent.

Units of radioactivity

The SI unit of radioactivity is the becquerel (Bq) and is equalto one nuclear disintegration per second.

A non-SI unit also in use is the curie (Ci), where 1 Ci = 3.7 × 1010 Bq

3.4 Artificial isotopes

Bombardment of nuclei by high-energy -particles and neutrons

Cyclotron (an accelerating machine)

transformations occur when nuclei are bombarded with high-energy neutrons or positively charged particles

t1/2= 3.2 min

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The bombardment of sulfur-32 with fast neutrons gives an artificial isotope of phosphorus

Bombardment of nuclei by ‘slow’ neutrons

High-energy (or ‘fast’) neutrons are produced by the nuclearfission of 235 92U and have energies of 1MeV

A thermal neutron has an energy of 0.05 eV.

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the production of artificial isotopes of elements that do not possess

naturally occurring radioisotopes.

the synthesis of the transuranium elements, nearly all of which are

exclusively man-made.

The transuranium elements (Z 93) are almost exclusively all

man-made. Other man-made elements include technetium

(Tc), promethium (Pm), astatine (At) and francium (Fr).

The transuranium elements (Z 93) are almost exclusively all

man-made. Other man-made elements include technetium

(Tc), promethium (Pm), astatine (At) and francium (Fr).

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Different nuclei show wide variations in their ability to absorb neutrons,

and also in their probabilities of undergoing other nuclear reactions cross-section

have very low cross-sections with respect to the capture of thermal neutrons

possess very high cross-sections

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3.5 Nuclear fission

The fission of uranium-235

typical example; once formed, yttrium-95 and iodine-138 decay by -particle emission with half-lives of 10.3 min and 6.5 s respectively.

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the sum of the mass numbers of the two fission products plus the neutrons must equal 236.

the sum of the mass numbers of the two fission products plus the neutrons must equal 236.

The average number of neutrons released per nucleus undergoing fission is 2.5 and the energy liberated (2 × 1010 kJ/mol of 235

92U) is about two million times that obtained by burning an equal mass of coal.

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Since each neutron can initiate another nuclear reaction, a branching chain reaction is possible.

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 235

92U nuclide

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The reaction must proceed with conservation of mass number and of charge.

Z = 92 42 = 50A = 235 + 1 103 2 = 131

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The production of energy by nuclear fission

The production of energy by nuclear fission in a nuclear reactor must be a controlled process.

Neutrons released from the fission of 23592U most lose of their kinetic energy

by passage through a moderator (graphite or D2O).

They then undergo one of two nuclear reactions.

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potentially catastrophic branching chain reaction is prevented by

controlling the neutron concentration in the nuclear reactor by

inserting boron-containing steel, boron carbide or cadmium

control rods.

The choice of material follows from the high cross-section for neutron capture exhibited by 10

5B and 11348Cd.

3.6 Syntheses of transuranium elements

All of these ‘new’ elements have been produced synthetically by

the bombardment of particular heavy nuclides with particles such

as neutrons and 12 6Cn+ or 18 8On+ ions

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3.8 Nuclear fusion

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

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Radiocarbon dating

The method relies on the fact that one isotope of carbon, 14 6C, is radioactive (t1/2= 5730 yr) and decays according to

In a living plant, the ratio of 14 6C : 12 6C is constant. Although carbon-14 decays, it is re-formed at the same rate by collisions between high-energy neutrons and atmospheric nitrogen-14

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The -activity of 1.0 g of carbon from the wood of a recently felled tree is 0.26 Bq. If the activity of 1.0 g of carbon isolated from the wood of an Egyptian mummy case is 0.16 Bq under the same conditions, estimate the age of the mummy case.(14C: t1/2= 5730 yr.)

dr. said m. el-kurdi1 nuclear properties chapter 3

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