8 Nuclear Instability (Transmutation)

7/28/2019 8 Nuclear Instability (Transmutation)

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Nuclear Instability

(Transmutation)


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Contents

Basic Radioactivity Inverse Square Law of Gamma Radiation

Exponential Law of Decay

Probing Matter


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Basic RadioactivityRadiation is the decay of an unstable parent nucleus to a more

stable daughter nucleus by emitting particles and/or energy

Transmutation is the process in which the unstable nucleus decays to form

another nucleus of a different atom. If this new nucleus is unstable, it willdecay again, and this is known as a decay chain.

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


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Basic Radioactivity

Isotopes of different elements may be radioactive. These

radioactive versions are called radioisotopes.

There are three types of radiation:

Radiation Description Penetration Ionisation Effect of E or Bfield

Alpha ()Helium nucleus

2p + 2nQ = + 2 e

Few cm airThin paper

Intense, about 104ion pairs per mm.

Slight deflection asa positive charge

Beta ()

High speed

electronQ = -1 e

Few mm of

aluminium

Less intense than

a, about 102

ionpairs per mm.

Strong deflection

in oppositedirection to a.

Gamma ()Very short

wavelength emradiation

Several cm lead,couple of m of

concrete

Weak interactionabout 1 ion pair

per mm.No effect.


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Inverse Square Law of Gamma Radiation

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

If Count Rate against 1/Distance2 isplotted, a straight line is achieved.

The origin of the line is below zerodistance because the gamma source

is deep within its housing.

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


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Inverse Square Law of Gamma RadiationThe 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 whenperforming 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, ifl0 is unknown:

&

When combined and rearranged gives:


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Exponential Law of DecayRadioactive decay is entirely randomand unpredictable.

Chemical reactions involve the outer shell of electrons, BUTradioactive decay involves the nucleus of an atom.

The rate of decay of any nuclide at a given time is directlyproportional to the number of atoms left at that time:

(The minus sign indicates that Ndecreases as time increases)

(The d/dt gives the rate of change)

Incorporating the radioactive decay constant, , 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


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Exponential Law of DecayThe units ofis s-1 (per second), but often the Becquerel is used:

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

Where: N no of nuclei N0 original number of nuclei

e exponential number

- decay constant t time(s)

This relationship is knownas exponential decay, andthe graph of this is shownhere

The rate of decay is theactivity, measured inBecquerels, Bq


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Exponential Law of DecayHalf-lifeDefined as the time taken for the activity of a sample to decreaseto 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


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Probing 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 electrondiffraction tube as shown above. A slice of carbon is placed in a beam of electronsso that the electrons diffract, producing diffraction ringswhich show their wave-like

properties


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Probing Matter X-Ray Diffraction

A sample of the material isplaced in the beam of X-rays,and the resulting scatteringpattern is picked up on aphotographic plate. The X raysare diffracted in a cone. It is

useful tool to discover thestructure of solid materials.

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

n = 2dsin

where: norder of diffraction - de Broglie wavelength of the x-raysd the distance from source to screen- diffraction angle (cone angle for this case)


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Probing Matter Nuclear Radius

Rutherford estimated the radiusof a nucleus from his scatteringexperiments, and using CoulombsLaw, 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


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Probing Matter Electron Scattering

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

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

where:

- de Broglie wavelength of the high-energy electrons

- angle of diffractionR - 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= r0A1/3r0- a constant, value: 1.410

-15 m

A - nucleon number

The graph represents thisrelationship between nuclear

radius and nucleon number

Nuclear radius is different toatomic radius.Atomic radius is similarwhether the element is light orheavy.Nuclear radius can vary

largely, depending on element


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Summary

Basic Radioactivity Inverse Square Law of Gamma Radiation

Exponential Law of Decay

Probing Matter

8 Nuclear Instability (Transmutation)

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