Nuclear Instability

1. Nuclear Instability

2. Contents • Basic Radioactivity • Inverse Square Law of Gamma Radiation • Exponential Law of Decay • Probing Matter

3. Basic Radioactivity Radiation 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 will decay again, and this is known as a decay chain. The decay chain be very long or very short. Some elements decay over thousands of years, some after microseconds.

4. Basic Radioactivity Isotopes of different elements may be radioactive. These radioactive versions are called radioisotopes. There are three types of radiation:

5. Inverse Square Law of Gamma Radiation To measure the variation of gamma ray intensity with distance, the above experiment is used. If Count Rate against 1/Distance2 is plotted, a straight line is achieved. The origin of the line is below zero distance because the gamma source is deep within its 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.

6. Inverse Square Law of Gamma Radiation The inverse square relationship is therefore: Where: I – intensity I0 – intensity at the source k – constant x – the distance from the source It is more common to calculate counts from two points, if l0 is unknown: When combined and rearranged gives: & 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)

7. Exponential Law of Decay Radioactive decay is entirely random and unpredictable. Chemical reactions involve the outer shell of electrons, 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”

8. Exponential Law of Decay The units of λis s-1 (per second), but often the Becquerel is used: 1 Bq = 1 count per second 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

9. Exponential Law of Decay Half-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

10. Probing Matter • Methods 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

11. Probing 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 sin where: 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)

12. Probing Matter • Nuclear Radius • Rutherford estimated the radius • of a nucleus from his scattering • experiments, and using Coulomb’s • Law, to be ~ 3.0x10-14 m • The particle is repelled at point P. • It has zero Kinetic Energy, as it is • stationary; all its energy is potential. • Using electrostatic potential energy equations, the distance can be calculated: Ep = potential at P × charge of the alpha particle: Therefore: rc= 3.25x10-14 m Rearrange:

13. Probing 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 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 r0 - a constant, value: 1.4×10-15 m A - nucleon number The graph represents this relationship between nuclear radius and nucleon number

14. Summary • Basic Radioactivity • Inverse Square Law of Gamma Radiation • Exponential Law of Decay • Probing Matter