Nuclear InstabilityNuclear Instability

ContentsContents

Basic RadioactivityBasic Radioactivity Inverse Square Law of Gamma Inverse Square Law of Gamma

RadiationRadiation Exponential Law of DecayExponential Law of Decay Probing MatterProbing Matter

Basic RadioactivityBasic RadioactivityRadiation is the decay of an unstable parent nucleus to Radiation is the decay of an unstable parent nucleus to a more stable daughter nucleus by emitting particles a more stable daughter nucleus by emitting particles

and/or energyand/or energy

TransmutationTransmutation is the process in which the unstable nucleus he unstable nucleus decays to form another nucleus of a different atom. If this new decays to form another nucleus of a different atom. If this new nucleus is unstable, it will decay again, and this is known as a nucleus is unstable, it will decay again, and this is known as a decay chain.decay chain.

The decay chain be very long or very short. Some elements decay The decay chain be very long or very short. Some elements decay over thousands of years, some after microseconds.over thousands of years, some after microseconds.

Basic RadioactivityBasic RadioactivityIsotopes of different elements may be radioactive. Isotopes of different elements may be radioactive.

These radioactive versions are called radioisotopes.These radioactive versions are called radioisotopes.

There are three types of radiation:There are three types of radiation:

Radiation Description Penetration Ionisation Effect of E or B field

Alpha (a) Helium nucleus

2p + 2n Q = + 2 e

Few cm air Thin paper

Intense, about 104

ion pairs per mm.

Slight deflection as

a positive charge

Beta (b) High speedelectron Q = -1 e

Few mm ofaluminium

Less intense than

a, about 102 ionpairs per mm.

Strong deflection

in oppositedirection to a.

Gamma (g) Very short

wavelength emradiation

Several cm lead,couple of m of

concrete

Weak interaction

about 1 ion pairper mm.

No effect.

Inverse Square Law of Gamma Inverse Square Law of Gamma RadiationRadiation

To measure the variation of gamma ray intensity with distance, the To measure the variation of gamma ray intensity with distance, the above experiment is used.above experiment is used.

If Count Rate against 1/DistanceIf Count Rate against 1/Distance22 is plotted, a straight line is is plotted, a straight line is

achieved.achieved.The origin of the line is below The origin of the line is below

zero distance because the zero distance because the gamma source is deep within its gamma source is deep within its

housing.housing.

It is found that the counts per second, intensity, decreases with the square of the distance, meaning if the distance is doubled, the intensity reduces by

four times.

Inverse Square Law of Gamma Inverse Square Law of Gamma RadiationRadiation

The inverse square relationship is therefore:

Where: I – intensity I0 – intensity at the source k – constant x – the distance from the source

Background Radiation – must be measured and taken into account when performing radiation experiments. It comes in the following forms:· Cosmic rays· Radioactive material in the bricks of the building.· Small amounts from medical and industrial uses.· People (contain Carbon-14 amongst other radioisotopes)

It is more common to calculate counts from two points, if l0 is unknown:

&When combined and rearranged

gives:

Exponential Law of DecayExponential Law of DecayRadioactive decay is entirely Radioactive decay is entirely random random and and

unpredictable.unpredictable.Chemical reactions involve the outer shell of electrons, Chemical reactions involve the outer shell of electrons, BUT radioactive decay involves the nucleus of an atom.BUT radioactive decay involves the nucleus of an atom.The rate of decay of any nuclide at a given time is

directly proportional to the number of atoms left at that time:

(The minus sign indicates that N decreases as time

increases)

(The d/dt gives the rate of change)

Incorporating the radioactive decay constant, λ, into this equation gives:

The radioactive decay constant is “the fraction of the total number of nuclei present that decays per unit time, provided that the time interval

is small”

Exponential Law of DecayExponential Law of DecayThe units of The units of λ is s-1 (per second), but often the Becquerel

is used:

1 Bq = 1 count per secondOver long time periods, the equation becomes:Over long time periods, the equation becomes:

Where: N – no of nuclei N0 – original number of nuclei e – exponential number λ - decay constant t – time(s)

This relationship is known as exponential decay, and the graph of this is shown here

The rate of decay is the activity, measured in Becquerels, Bq

Exponential Law of DecayExponential Law of DecayHalf-life Defined as “the time taken for the activity of a sample to decrease to half of some initial value” So:

After 1 half life Activity=50%After 2 half lives Activity=25%After 3 half lives Activity=12.5%

etc...

Half-life can be related to the decay constant:By definition:- and:-

Therefore:-

Half-life is useful for ascertaining methods of storing radioactive waste.

The decay equations are useful for radioactive dating, using radioisotopes such as carbon-14, rubidium-87, and hydrogen-3

Probing MatterProbing MatterMethods of probing matter:

• Rutherford scattering (described in “Particles, Radiation & Quantum Phenomena”)

• Electron diffraction tube

Electrons can be shown to have simple wave properties by using an electron diffraction tube as shown above. A slice of carbon is placed in

a beam of electrons so that the electrons diffract, producing diffraction rings which show their wave-like properties

Probing MatterProbing Matter• X-Ray Diffraction

A sample of the material is placed in the beam of X-rays, and the resulting scattering pattern is picked up on a photographic plate. The X rays are diffracted in a cone. It is useful tool to discover the structure of solid materials.

Using a simple equation, the separation of layers of atoms can be determined:

n = 2d sinwhere: n – order of diffraction - de Broglie wavelength of the x-rays

d – the distance from source to screen - diffraction angle (cone angle for this case)

Probing MatterProbing Matter• Nuclear Radius

Rutherford estimated the radiusof a nucleus from his scatteringexperiments, and using Coulomb’sLaw, to be ~ 3.0x10-14 m

The particle is repelled at point P.It has zero Kinetic Energy, as it isstationary; all its energy is potential.

Using electrostatic potential energy equations, the distance can be calculated:

Ep = potential at P × charge of the alpha particle:

Rearrange: Therefore: rc = 3.25x10-14 m

Probing MatterProbing Matter• Electron Scattering

Electrons interact with the nucleus by electromagnetic interaction unlike the alpha particles which interact by strong nuclear interaction.

A reasonable estimate can be obtained with a fairly simple equation:

where: λ - de Broglie wavelength of the high-energy electrons θ - angle of diffraction

R - nuclear radius

This gives a result of the radius being: 2.65 × 10-15 m

However, the radius depends on the nucleon number via a simple relationship: R = r0 A 1/3

r0 - a constant, value: 1.4×10-15 m

A - nucleon number

The graph represents this relationship between nuclear radius and nucleon number

Nuclear radius is different to atomic radius.Atomic radius is similar whether the element is light or heavy.Nuclear radius can vary largely, depending on element

SummarySummary

Basic RadioactivityBasic Radioactivity Inverse Square Law of Gamma Inverse Square Law of Gamma

RadiationRadiation Exponential Law of DecayExponential Law of Decay Probing MatterProbing Matter