Isotope 2 Flashcards
Nuclear Systematics - Isotopes
Isotones: Two nuclides that have the same neutron number N, but different proton number Z
Isotope: Atoms of same element = same atomic number but have different mass
Stable nuclides = will not decay
Isobar: Atoms of different elements but have the same mass
• Even/Even – most abundant nuclides on Earth
• Only odd nuclides are low mass
• Z/N = proton neutron ratio
Unstable or radioactive elements
• There are 288 natural isotopes of which ~253 show no evidence of radioactive decay
• ~60% of these have:
o Even numbers of protons and/or even numbers of neutrons
o In general, they are the most abundant isotopes on earth
• Remaining ~40% of isotopes are about equally divided between:
o Even number of protons and odd number of neutrons
o Odd number of protons and even number of neutrons.
o Plotting neutron number (A) against proton number (Z) for all known nuclei, shows area of stability.
o For very light elements Z/N =1 gives stable elements up to 4020Ca.
o Z/N ratio gradually decreases until by element 83 (Bi, the last one with a ‘stable isotope’) it is ~0.67.
o At higher atomic number stability of a nuclide is favoured by being neutron-rich.
o Stability of a nuclide is clearly favoured by even numbers of protons and neutrons BUT not usually equal numbers.
Why even/even = more stable?
o Protons have +ve charge and therefore repel one another: Coulomb repulsion.
o Neutrons are neutral and produce attractive forces within nuclei: Strong nuclear force
o As the number of protons increases an excess of neutrons is required to overcome the proton-proton repulsion
The Shell model:
• Each nucleon is assumed to exist in a shell similar to atomic shells for electrons
• The nucleons exist in quantized energy states. Each state can contain only two protons or two neutrons
They must have opposite spins
They have spins of ½, so the exclusion principle applies
• Protons and Neutrons occupy separate sets of energy states
• Nuclei with even numbers of protons and neutrons are more stable. Any particular state is filled when it contains two protons or two neutrons
• An extra proton or neutron can be added to the nucleus only at the expense of increasing the nucleus’s energy. This energy increase leads to greater instability in the nucleus.
Adding proton or neutron = beta decay
Alpha decay
• Parent isotope (radioactive isotope)
• Daughter – formed by radioactive decay (radiogenic)
• Parent loses an alpha particle (helium nucleus)
• Z goes down by 2, N goes down by 2
• Sm 14762 to Nd 143, 60
o Mass number down by 2, Z down by 2
• Loss of 2 protons and 2 neutrons
Beta decay
• Parent loses neutron • N goes down by 1 Decays into proton and electron Electron is removed • Proton goes up by 1 • Mass number therefore stays the same ( Z+1, N-1) • = isobar • Loss of neutron
Electron Capture
- Proton dissociates from parent
- Proton captures electron and converts to neutron
- Atomic number goes down by 1
- Loss of proton
Isotope decay diagram
- Proton rich = want to capture an electron to increase neutron number
- Neutron rich = beta decay
Isochron equation
• If the number of daughter atoms in a sample at time zero is D0 then the total number of daughter atoms (D) after decay of the unstable parent (N) after time t is given by this equation:
D=Do+N(e^lamda*t - 1)
• Assuming D and N can be measured and D0 determined, the equation can be solved for the age ‘t’ as long as the decay constant l (or T1/2) for the element in question is known.
Isochron assumptions
• To use radioactive decay and the isochron equation to date rocks there are two basic assumptions we have to make (often challenged by creationists).
o 1. The decay constant for the element is known.
o 2. The decay constant for the element has not changed over time.
The decay constant for the element is known.
The decay constant for the element has not changed over time.
Decay is a purely random process
Methods for determining the decay constant of an unstable isotope overview
The decay constant for the element is known.
Direct counting
Daughter isotope measurement:
Geological comparison
Methods for determining the decay constant of an unstable isotope (DC)
Direct counting:
- Number of spontaneous decays on pure element can be counted.
- Several drawbacks to this method: abundance of unstable isotope may be very low and/or the decay constant is very low (e.g. 176Lu) so counting times may need to be long.
Over this period, detector reliability becomes an issue. Also, erroneous counts due to cosmic rays?
- For some elements the unstable isotope (e.g. 87Rb) emits low energy particles, which can be absorbed before they reach the detector – resulting in underestimate of the decay constant.
Methods for determining the decay constant of an unstable isotope (DI)
Daughter isotope measurement:
- Accumulation of daughter isotope in a sample of the parent element is directly proportional to the number of parent atoms that decay, so amount of daughter can be measured.
- As with direct counting, this method can take years but no counting is necessary and the sample can just be left in a sealed container for the desired time. At time zero (the start of the experiment) the sample must contain no daughter atoms or at least the quantity must be accurately determined.
Methods for determining the decay constant of an unstable isotope GC
Geological comparison:
- Decay constants for some elements are easier to determine by direct counting than others (e.g. U). If these elements are used to date a suite of rocks then the decay constants for other elements can be determined from those samples because the age t is known. The disadvantage is that it is best carried out on old rocks (often meteorites are used), which are usually associated with the greatest geological uncertainties (alteration, metamorphism and closure temperatures). (The concept of closure temperatures will be introduced next week). Nevertheless provides a useful check on laboratory measurements.
Processes to determine that the decay constant for the element has not changed over time.
Demonstrated in several ways:
• Direct measurement, under extreme conditions
• Frequencies and fading rates of gamma ray emissions from type Ia supernovae going back over several billion years are predictable according to present-day decay rates – i.e. no observable change
• Different isotope systems give consistent ages
• Highly fortuitous if decay rates are not constant
• Oklo natural nuclear reactor – 1.7 Ga
• Constant (as far as we can tell) nuclear behaviour over last 1.7 Ga
• Oklo shows decay constant is constant over time
