Radioactive decay and unstable nuclides
A,Z,N, isotopes, isotones, isobars, and the Valley of Beta stability
Z is the number of protons in a nucleus (also the atomic number)
N is the number of neutrons
A is the atomic mass number, where A=Z+N
146C is carbon with atomic number 6 (Z=6) and atomic mass number 14 (A=14); thus, N=A-Z=14-6=8.
Isotopes are nuclides (atoms) of the same atomic number (Z). In other words different masses of the same element.
For example, Sulfur has 10 isotopes. (See chart of the nuclides up close.) 4 of these isotopes are stable (32S, 33S, 34S, and 36S). In the chart of the nuclides the percent abundance in nature of the stable isotopes is given as the second line. Thus 32S= 95.0%, 33S=0.75%, 34S=4.2%, and 36S=0.015%. For the unstable isotopes the halflife is displayed on the second line. Thus, 35S has a t1/2=87.2 days.
Isotopes, Isotones and Isobars
Isotones have the same amount of neutrons (same N).
Chart of the nuclides and valley of beta stability
Chart of the nuclides is a plot of the nuclides in Z vs. N (Y vs. X axis).
Radioactive decay
Nuclides that are unstable will decay to stable nuclides given enough time. How these atoms decay can be displayed graphically on the chart of the nuclides. There are 5 main mechanisms that a nuclide will undergo radioactive decay to a stable nuclide.
Beta decay- An unstable nuclide undergoes decay by emitting an electron. Enrico Fermi proposed that beta decay is equivalent to the transformation of a neutron into a proton and an electron. The electron is then expelled from the nucleus as a negatively charged beta particle. This nuclear reaction also produces a neutrino, an atomic particle with negligilbe (or no) mass, no charge, and interacts sparingly with matter, such that the energy of this particle is released to space.
40K decays to 40Ca by beta decay. This reaction can be written as:
4019K --> 4020Ca + B- + v- + Q, where B- is a beta particle, v- is an antineutrino, and Q is the maximum decay energy.
Positron decay-An unstable nuclide undergoes decay by emitting a positron (a positive charged electron). According to Fermi's theory the unstable nuclide undergoes transformation in the nucleus of a proton to a neutron, a neutrino, and a positron (a positive charged Beta particle).
Alpha decay-An unstable nuclide undergoes decay by emitting an alpha particle, which is essentially a 4He nuclei. This is a much larger particle than an electron or positron, with 2 protons and 2 neutrons.
Electron capture-An electron from the nearest electron shell (the K shell) is captured by the nucleus (though electrons from other shells can be captured also). The reaction is a proton and extranuclear electron form a neutron and a neutrino. On the nuclide chart, this would be similar to positron decay.
Nuclear Fission-A nuclide can undergo spontaneous fission into 2 or more nuclides and atomic fragments.
Exponential decay N=No e-lt
Units of Radioactivity and dosage
A is the observed activity of a radioactive sample in disintegrations per unit time, where A=clN, where lN is the actual rate of decay and c is a instrumental coefficient.
clN=clNoe-lt
A=Aoe-lt
lnA=lnAo - lt
Basic unit of radioactivity is the Curie (Ci) which is defined as quantity of radioactive nuclide in which the number of disintegrations is 3.7x1010 per second.
Carbon 14 and Tritium (3H)
Carbon 14 and tritium are both produced naturally by the interactions of cosmic rays with the upper atmosphere gaseous molecules. The cosmic rays are energetic particles (primarily protons and alpha particles) that originate in the Sun or in our nearby galaxy. Tritium is also a byproduct of nuclear bombs. Tritium reached a peak in 1964 due to extensive nuclear testing in 1961-1963. This 'seeding' of the atmosphere with tritium (as well as other nuclide byproducts of nuclear bombs) allowed earth, atmospheric and ocean scientists to have 'tracers' in the atmosphere and oceans (for example tritium replaces hydrogen to become water) to trace atmospheric and oceanic circulation and the timescales associated with atmospheric and oceanic mixing.
Carbon 14 is the world's most famous dating tool. 14C has a t1/2=5730±40 years which allows it to be used to date archeological finds. 14C is formed by a number of cosmic ray interactions (called 'spallation' reactions), but the most important is as a result of slow neutrons and stable 14N:
10n + 147N --> 146C + 11H
The decay of 14C occurs by beta decay to 14N.
The radioactivity of a plant or animal sample is determined by:
A = Aoe-lt, where A is the activity measured due to 14C in units of disintegrations per minute per gram of carbon, and Ao is the activity when the plant or animal died (initial condition). During a plant or animal's life the 14C is a steady state due to continued ingestion of 'fresh' 14C. 14C is formed in the upper atmosphere and reaches equilibrium with atmospheric CO2 which gives a steady-state activity of 14C for the atmosphere. Plants maintain this equilibrium. Animals eat plants (or other animals that ate plants somewhere in the food chain) which maintains a steady state activity of 14C in living organisms.
