Nuclear Physics

Radioactivity Properties of α, β and γ radiations Detectors Random nature of decay Natural nuclear deformation Radiation Hazards

The Nucleus The Rutherford model of the atom Mass-energy relationship Binding energy Fission and fusion

Decay Series

It is often the case that one radioactive isotope decays to another isotope that is also radioactive. Such successive decays are said to form a decay series.

Properties of , and radiations (1)

0-1+2Charge

Electro-magnetic waves

Fast-moving electrons

Helium nucleiNature

Increasing the stability by emitting –rays.

Altering the Z/N ratio to achieve greater stability.

Increasing the stability by reducing the size and charge of the nuclei.

Occurrence

-rays -particles-particles

Very weak (0.01% of )

Weak

(10% of )StrongIonizing

ability

No deflectionLarge deflection

Very small deflection

Effect of Fields

Speed of lightUp to 90% speed of light

Up to 10% speed of light

Speed

01/18504Mass (nucleon unit)

Properties of , and radiations (2)

Properties of , and radiations (3)

0.01 – 10 0.01 – 10 0.5 – 1.0Energy

(MeV)

Never fully absorbed : reduced to half by 25 mm of lead

Stopped by

5 mm of aluminium

Stopped by a sheet of paper

Penetrating power

~500 m~5 m~5 cmRange in air

Properties of , and radiations (4)

No transmutation

Radioactive transmutation

Photographic

filmCloud chamberGM tube

Photographic

filmCloud

chamberGM tube

Photographic

filmIonization

chamberCloud chamberSpark counterThin window

GM tube

Detectors

HeYX AZ

AZ

42

42

eYX AZ

AZ

011

Radiation Detectors

Photographic Film To detect , and radiations

Spark counter To detect -particles

Ionization Chamber To detect -particles

Cloud Chamber To detect and particles

Geiger-Müller Tube To detect , and radiations

Photographic Film

The photographic film has been blackened by radioactivity except in the shadow of the key.

Spark Counter

The spark counter consists of positively charged wire mounted under an earthed metal grid.

It produces sparks in the presence of ionized particles.

It can only be used to detect α-radiation.

Earthed grid

To the positive terminalof the EHT supply

Ionization Chamber (1)

A diagram of the ionization is drawn in the diagram below.

2 kV μAR

Radioactivesource

Central electrode

Conducting can

Insulating cap

Ionization Chamber (2)

The number of ions produced per second by the source of ionizing radiation can be estimated from the current flowing. This estimate depends on the following conditions: The ionization chamber must be sufficiently large to

enable the radiation to travel its full range. The electric field must be large enough to ensure that all

the ions travel to the electrode before recombining with free electrons.

The ionization chamber can only be used to detect α-particles.

Cloud Chamber (1)

The diagrams below show a diffusion cloud chamber and its structure.

Cloud Chamber (2)

The felt strip round the top of the chamber is soaked with alcohol.

The solid CO2 cools the chamber to a low temperature.

The alcohol vapour condensed on the ions caused by the passage of -particles.

A jet trail is left behind.

Cloud Chamber Tracks (1)

Cloud Chamber Tracks (2)

Cloud Chamber Tracks (3)

Under diffusion cloud chamber, Alpha source gives thick , straight tracks ; Beta source produces thin, twisted tracks. They

are small in mass and so bounce off from air molecules on collision.

Gamma source gives scattered, thin tracks. Gamma rays remove electrons from air molecules. These electrons behave like beta particles.

GM Counter

When ionizing radiation enters the GM tube, ions and free electrons are formed.

A flow of charge takes place and causes a pulse of current.

The pulse of current is amplified and counted electronically.

Activity of a radioactive isotope (1)

Let N(t) be the number of radioactive nuclei in a sample at time t.

)()(

tkNdt

tdN

The decay rate is directly proportional to N(t).

dt

tdN )(Decay rate (Activity) =

The constant k is called the decay constant. A large value

of k corresponds to rapid decay.

The `-’ sign indicates that N(t) decreases with time

The SI unit of activity is the becquerel (Bq).

Activity of a radioactive isotope (2)

k can be interpreted as the probability per unit time that any individual nucleus will decay.

Since this also gives Ndt

tdN

)( ktt e

dt

tdN

dt

tdN 0))(

())(

(

ktoeNtN )(

where No is the number of nuclei present at t = 0.

)()(

tkNdt

tdNSolving the equation to get

Half-life (1)

The graph shows the number of remaining nuclei N(t) as a function of time.

Half-life (2)

The half-life t1/2 is the time required for the number of radioactive nuclei to decrease to one-half the original number No.

At t = t1/2, N(t) = No/2, obtaining2

12/1 kte

Taking logarithms to base e, gives

kkt

693.02ln2/1

Uses of Radioactive Isotopes (1)

Medicine Treating cancer

Brachytherapy Gamma-therapy

Tracers Surgical sterilisation Pacemaker

IndustrySmoke detectorThickness gaugeSterilisationRadioactive lightning conductorDetection of leakageFlaw detection

Uses of Radioactive Isotopes (2)

Agriculture Genetic improvement Pest control Tracers

Archaeology Carbon-14 dating Geological dating

Military affairs Atomic bomb Hydrogen bomb

Radiation Hazards (1)

Dose The energy transferred by radiation to materials is

called radiation dose. The radiation dose measured in grays (Gy). 1 gray is equal to one joule of energy transferred to each

kg of material. Equal exposure to different types of radiation do not

necessarily produce equal biological effects so we use sieverts (Sv) to measure the radiation effect.

One sievert of radiation produces a constant biological effect regardless of the type of radiation.

Radiation Hazards (2)

Background radiation Natural radiation

sources Man-made radiation

sources

Dose from background radiation (1)

Source Dose (mSv/year)

Natural radiation sources

External irradiation:

Cosmic rays (sea level) 0.28

Inside brick and concrete buildings 0.78

Radon in air 0.01

Internal irradiation:

Potassium-40 0.2

Carbon-14 0.01

Radon+disintegration 0.02

Dose from background radiation (2)

Source Dose (mSv/year)

Man-made radiation sources

Fall-out 0.07

Medical exposures

Chest X-ray 0.5

Gastro-intestinal examination with fluoroscopy

8

Luminous compounds 0.4

Television sets up to 0.04

How much radiation is dangerous?

The diagram gives an indication of the likely effects and implications of a range of radiations and does rates to the whole body.

Sealed and unsealed sources used in schools

Sealed sources Amercium-241 ( and -emitter) Cobalt-60 ( and -emitter) Radium-226 ( and -emitter) Strontium-90 (-emitter)

Unsealed sources Uranyl nitrate Natural thorium

Hazards due to sealed and unsealed sources (1)

Hazards due to sealed sources α-particles usually do not present any external

radiation hazard because they are unable to penetrate to dead layer of skin. But, extremely precautions must be taken to prevent α-emitters from getting into the body.

β-particles never constitute a whole-body external radiation hazard due to their short range in tissue.

γ-rays have very high penetrating power and require greater care to avoid receiving excess dosage.

Hazards due to sealed and unsealed sources (2)

Hazards due to unsealed sources Unsealed sources usually constitute some kind

of internal hazard. This is the absorption and retention of radionuclides into specific organs of the body through intake of the materials present in air and in water.

The radionuclides may be rapidly absorbed by the organs causing damage to these organs.

Handling precautions

The weak sources used at school should always by lifted with forceps.

The sources should never by held near the eyes. The source should be kept in their boxes when not

in use. The strong sources should be handled by long

tongs and transported in thick lead containers. Workers should be protected by lead and concrete

walls and wear radiation dose badges which keep a check on the amount of radiation they have been exposed to.

Alpha-Scattering Experiment (1)

A beam of -particles was directed at a thin sheet of gold-foil and the scattered -particles were detected using a small zinc sulphide screen viewed through a microscope in a vacuum chamber. Side

view

To vacuum pump

Evacuated metal box

-source

Gold foilZinc sulphidescreen

microscope

Alpha-scattering Experiment (2)

From the experiment it was found that

a few were deflected at very large angles,some were nearly reflected back in the direction from which they had come.

most of the -particles passed through the foil unaffected,

Rutherford’s atomic model

Rutherford’s assumptions: All the atom’s positive charge is concentrated

in a relatively small volume, called the nucleus of the atom

The electrons surround the nucleus at relatively large distance. Most of the atom’s mass is concentrated in its nucleus.

10-15 m

10-10 m

Difficulties of Rutherford’s model

The Rutherford model was unable to explain why atoms emit line spectra. The main difficulties are: It predicts that light of a

continuous range of frequencies will be emitted;

It predicts atoms are unstable—electrons should quickly spiral into the nucleus.

Mass and Energy

The mass-energy relationship Einstein showed that mass and energy are

equivalent. E = mc2

Mass defect The difference between the mass of an atom and

the mass of its particles taken separately is called the mass defect (Δm).

Δm = Zmp +Nmn- Mnucleus

The mass defect is small compared with the total mass of the atom.

Unified Atomic Mass Unit

The unified atomic mass unit (u) is defined as one twelfth of the mass of the carbon atom which contains six protons, six neutrons and six electrons.

1 u = 1.660566 × 10-27 kg Energy equivalence of mass

1 u = 931.5 MeV It is a useful quantity to calculate the energy

change in nuclear transformations.

Binding Energy (1)

The energy required to just take all the nucleons apart so that they are completely separated is called the binding energy of the nucleus.

Binding Energy (2)

From Einstein’s mass-energy relation, the total mass of all separated nucleons is greater than that of the nucleus, in which they are together. The difference in mass is a measure of the binding energy.

According to relativity theory, total binding energy = Δmc2

where Δm is the mass defect of the nucleus.

Binding Energy (3)

Binding energy of Helium

m = 4.0330 u - 4.0026 u = 0.0304 u

E = 28.3 MeV

Binding energy per nucleon = 7.08 MeV per nucleon

Binding Energy (4)

The values of the binding energy varies from one nuclear structure to another.

The greater the binding energy per nucleon, the more stable the nuclei.

Binding Energy Curve (1)

The graph shows the variation of the binding energy per nucleon among the elements.

Fission

Fusion

Binding energy Curve (2)

The important features of the binding energy curve: Maximum binding energy per nucleon is at about

nucleon number A = 50. Maximum binding energy per nucleon corresponds to the most stable nuclei.

Either side of maximum binding energy per nucleon are less stable.

Binding Energy Curve (3)

When light nuclei are joined together, the binding energy per nucleon is also increased. So energy is released when light nuclei are fused together.

When a big nucleus disintegrates, the binding energy per nucleon increases and energy is released. So fission or radioactive decay both lead to an increase of binding energy per nucleon and hence to release energy as KE of the product.

Principles of Nuclear Fission (1)

Nuclear fission is a decay process in which an unstable nucleus splits into two fragments of comparable mass.

nKrBanU 10

8936

14456

10

23592 3 + energy released

nSrXenU 10

9438

14054

10

23592 2 + energy released

Two typical nuclear fission reactions are:

Principles of Nuclear Fission (2)

Further investigations showed that several neutrons are released with the fission

fragments, many fission products are possible when U-235 is

bombarded with neutrons, the products themselves are radioactive, slow neutrons are more effective in fissioning U-235

than fast neutrons, energy is released on much greater scale than is

released from chemical reaction.

Chain Reactions

Fission of uranium nucleus, triggered by neutron bombardment, released other neutrons that can trigger more fission. Chain reaction is said to occur.

http://www.smartown.com/sp2000/energy_planet/en/trad/fission.html#

Nuclear Power Plant

A power plant with cooling tower

Nuclear Reactor (1)

The schematic diagram of a nuclear reactor is shown below:

http://www.ae4rv.com/games/nuke.htm

Nuclear Reactor (2)

Enriched uranium is used as the fuel. The fuel is in the form of rods

enclosed in metal containers. A moderator is used to slow down

fission neutrons. Control rods are used to absorb

neutrons to maintain a steady rate of fissioning.

A coolant is pumped through the channels in the moderator to remove heat energy to a heat exchanger.

Processes inside the Nuclear Reactor

Each fission of U-235 nucleus produces fission fragments including neutrons. The fission fragments carry away most of the KE and transfer the KE to other atoms that they collide with. So the fuel pin get very hot.

The fission neutrons enter the moderator and collide with moderator atoms, transferring KE to these atoms. So the neutrons slow down until the average KE of a neutron is about the same as that of a moderator atom.

Slow neutron re-enter the fuel pins and cause further fission of U-235 nuclei.

Important features in the design of a nuclear reactor (1)

The critical mass of fuel required The critical mass of fuel is the minimum

mass capable of producing a self-sustaining chain reaction.

The fission neutrons could be absorbed by the U-238 nuclei without producing further fission.

The fission neutron could escape from the isolated block of uranium block without causing further fission.

Important features in the design of a nuclear reactor (2)

The choice of the moderator The atoms of an ideal moderator should have the

same mass as a neutron. So a neutron colliding elastically with a moderator atom would lose almost all its KE to the moderator atom.

In practice, graphite or heavy water (D2O) is chosen as the moderator.

The moderator atoms should not absorb neutrons but should scatter them instead.

Important features in the design of a nuclear reactor (3)

The choice of control rods The control rods absorb rather than scatter

neutrons. Boron and cadmium are very suitable

elements for control rods. Control rods are operated automatically.

Important features in the design of a nuclear reactor (4)

Coolants should ideally have the following properties: The coolant must have high heat transfer coefficient. The coolant must flow easily. The coolant must not be corrosive. Coolant atoms may become radioactive when they pass

through the core of the reactor. So the coolant must have low induced radioactivity.

The coolant must be in a sealed circuit.

Important features in the design of a nuclear reactor (5)

The treatment of waste The fuel rods are stored in containers in cooling

ponds until their activity has decreased and they are cooler.

The spent fuel is removed from the cans by remote control. The fuel is then reprocessed to recover unused fuel.

the unwanted material is then stored in sealed containers for many years until the activity has fallen to an insignificant.

Nuclear Fusion

Fusion is combining the nuclei of light elements to form a heavier element. This is a nuclear reaction and results in the release of large amounts of energy!

Energy is released due to the increase in binding energy of the product of the reaction.

In a fusion reaction, the total mass of the resultant nuclei is slightly less than the total mass of the original particles.

Example of Nuclear Fusion

An example of nuclear fusion can be seen in the Deuterium-Tritium Fusion Reaction.

MeVnHeHH 6.1710

42

31

21

Conditions for a Fusion Reaction (1)

Temperature Fusion reactions occur at a sufficient rate only at very high

temperature. Over 108 oC is needed for the Deuterium-Tritium reaction.

Density The density of fuel ions must be sufficiently large for fusion

reactions to take place at the required rate. The fusion power generated is reduced if the fuel is diluted by impurity atoms or by the accumulation of Helium ‘ash’ from the fusion reaction.

As fuel ions are burnt in the fusion process they must be replaced by new fuel and the Helium ash must be removed.

Conditions for a Fusion Reaction (2)

ConfinementThe hot plasma must be well isolated away from material surfaces in order to avoid cooling the plasma and releasing impurities that would contaminate and further cool the plasma.

In the Tokamak system, the plasma is isolated by magnetic fields.

Advantages of Nuclear Fusion

Abundant fuel supply No risk of a nuclear accident No air pollution No high-level nuclear waste No generation of weapons material

Nuclear Waste

Some waste is stored on asphalt pads in drums.

Storage Tanks for Nuclear Waste

These storage tanks were constructed to store liquid, high-level waste. After construction was completed, the earth was replaced to bury the tanks underground.

Nuclear Stability (1)

The Segrè chart below shows neutron number and proton number for stable nuclides.

For low mass numbers, NZ.The ratio N/Z increases with A.Points to the right of the stability region represents nuclides that have too many protons relative to neutrons.To the left of the stability region are nuclides with too many neutrons relative to protons.

Nuclear Stability (2)

Nuclear Stability (3)

Deflection of α, β and γ rays in electric and magnetic fields (1)

α

-

+

β

γ

Deflection in electric field Deflection in magnetic field

Deflection of α, β and γ rays in electric and magnetic fields (2)

Under the effect of electric field or magnetic field, (in the direction of going into the paper); α-ray shows small deflection in an upward direction; β-ray shows a larger deflection than that of alpha

ray, and in a downward direction; γ-ray shows no deflection.

Penetrating Power

The diagram below shows the apparatus used to deduce the penetrating abilities of α, β and γ radiations.

Moderator

Use materials that slow the neutrons down to such low energies at which the probability of causing a fission is significantly higher. These neutron slowing down materials are the so called moderators.

http://www.npp.hu/mukodes/lancreakcio-e.htm

umM

Mmv

umM

mV

2

Control rods

reactor core at the bottom of a 5 m deep tank of very pure water

Reactor core glowing at full licensed power