2 - introduction to isotopes and what they are Flashcards
isotopes
atoms of the same element that vary in mass due to different number of neutrons
(horizontal)
isobar
atoms of different elements with different no. protons and neutrons but the same overall mass balance (diagonal?)
isotone
atoms of different elements, different protons and neutrons (vertical)
becoming neutron heavy means
increasing autonomic number (right of the line)
what elements are radioactive
most elements are not
only certain elements isotopes
253/288 natural isotopes so no evidence of radioactive decay
60% of natural isotopes have..
.. Even number of protons and/or neutrons
in general are the most abundant isotopes on earth
40% of natural isotopes have…
… even number of protons and odd number of neutrons
… odd number of protons and even number of neutrons
4 stable nuclei
odd number of protons and neutrons - all with relatively low numbers:
(2/1)H, (6/3)Li, (10/5)B, (14/7)N
elements with an ??? Z have more stable isotopes
EVEN
area of stability
plot A against Z for all known nuclei
Z/N ratio gradually ???? until element ??
decreases
83 (Bi, the last on with a stable isotope)
at high Z stability of a nuclide is favored by being …
… neutron rich
stability of a nuclide is favored by …
… even number of protons and neutrons but not usually equal numbers
coulombrepulsion
protons have positive charge so repel one another
as increasing number of protons, an excess of neutrons is required to over come the proton-proton repulsion
strong nuclear force
neutrons are neutral and produce attractive forces with nuclei
strong neutron force happens over a very short length scale, must be a lot closer than with Coulomb 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 neutrons
- they must have opposite spins
- they must have spire of 1/2 therefore the exclusion principal applies
protons and neutrons occupy separate sets of energy sets
radio activity - Alpha (a) decay
involves a parent isotope (the radioactive isotope that goes under decay) to create the daughter/radiogenic isotope
loosed a particle - two protons, two neutrons - so both Z&N decry by 2
the decay scheme - down to left
alpha decay always has a slope of +1, from upper right to lower left
Radio activity - B decay
one of the neutrons is an outer energy unstable half energy state
parent loses a neutron (N down by 1) and the neutron is converted to a proton (Z increase by 1)
mass no. remains the same
Parent - daughter = isobars
decay scheme = up left (?)
Radio activity - electron capture
proton (from parent) dissociated/loses/ejects a proton
proton changes to a neutron
-1Z, +1N
potassium Aragon dating
down right decay scheme (?)
valley of stability
further away from central axis the slope gets steeper
stable elements at base of valley
electron capture, proton rich left hand side of the valley
1902 Rutherford and saddy
rate of decay of an unstable parent isotope is proportional to the number of atoms of the parent present at any time
-dN/dt proportional N
the proportionality can be replaced with a decay constant lamda, this constant lamda represents the probability that an atom will decay within a stated period of time
-dN/dt = lamda N
can also think of radioactive decay in terms of how long it takes for half the number of radioactive atoms present in a sample to decay
Half life can then be derived from the decay constant for any element using;
T1/2 = ln2/lamda = 0.69315/lamda
isochron equation
if the number of daughter atoms in a sample at a time zero is Do, then the total number of daughter atoms (D) after the decay of the unstable parent (N) after time t is given by:
D = Do + N (e (^lamda t) - 1)
IMPORTANT
is the fundamental basis of geochronological dating methods using radiogenic isotopes
D & N can be measured, Do determined
the equation can be solved for the age ‘t’ as long as the decay constant lamda or T1/2 fir the element in question is known
two basic assumptions made when using radioactive decay and isochron equation to date rocks
- the decay constant for the element is known
2. the decay constant for the element has not changed over time
methods for determining the decay constant of an unstable isotope
- direct counting g
- daughter isotope measurement
- geological comparison
direct counting method (method for determining decay constant of an unstable isotope)
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
daughter isotope method (method for determining decay constant of an unstable isotope)
(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 isotope can be measured. As with the direct counting 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 0 time (start) the sample must contain no daughter atoms or the quantity must be accurately determined)
geological comparison (method for determining decay constant of an unstable isotope)
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.
demonstrating the decay constant for the element has not changed over time, several ways
direct measurement, under extreme conditions
frequencies and fading rates of gammer ray emissions from a supernovae over several billion years are predictable according to present day roles - no observable change
different isotope systems give constant ages, highly fortuitous if decay rates aren’t constant
Okionatural nuclear reactor (1.7 Ga (long nuclear behavior) - constant as far as we can tell
The Oklo natural nuclear reactor
The radioactive decay rates of nuclides used in radiometric dating have not been observed to vary since their rates were directly measurable, at least within limits of accuracy. This is despite experiments that attempt to change decay rates (Emery 1972). Extreme pressure can cause electron-capture decay rates to increase slightly (less than 0.2 percent), but the change is small enough that it has no detectable effect on dates.Supernovae are known to produce a large quantity of radioactive isotopes (Nomoto et al. 1997a, 1997b; Thielemann et al. 1998). These isotopes produce gamma rays with frequencies and fading rates that are predictable according to present decay rates. These predictions hold for supernova SN1987A, which is 169,000 light-years away (Knödlseder 2000). Therefore, radioactive decay rates were not significantly different 169,000 years ago. Present decay rates are likewise consistent with observations of the gamma rays and fading rates of supernova SN1991T, which is sixty million light-years away (Prantzos 1999), and with fading rate observations of supernovae billions of light-years away (Perlmutter et al. 1998).The Oklo reactor was the site of a natural nuclear reaction 1,800 million years ago. The fine structure constant affects neutron capture rates, which can be measured from the reactor’s products. These measurements show no detectable change in the fine structure constant and neutron capture for almost two billion years (Fujii et al. 2000; Shlyakhter 1976).Radioactive decay at a rate fast enough to permit a young earth would have produced enough heat to melt the earth (Meert 2002).Different radioisotopes decay in different ways. It is unlikely that a variable rate would affect all the different mechanisms in the same way and to the same extent. Yet different radiometric dating techniques give consistent dates. Furthermore, radiometric dating techniques are consistent with other dating techniques, such as dendrochronology, ice core dating, and historical records (e.g., Renne et al. 1997).The half-lives of radioisotopes can be predicted from first principles through quantum mechanics. Any variation would have to come from changes to fundamental constants. According to the calculations that accurately predict half-lives, any change in fundamental constants would affect decay rates of different elements disproportionally, even when the elements decay by the same mechanism (Greenlees 2000; Krane 1987).
decay is a …
purely random process
radioactivity is a …
one way street, can’t convert back to parent
precision
how close a series of measurements are to one another
accuracy
how close a series of measurements are to the true/known/accepted value
need standards to prove the accuracy of labs
Radioactive decay is constant:
- rate given by decay constant Lamda,
or - by time it takes for half the parent isotope to decay to the daughter isotope: (half-life)
Equation defining decay of Parent and production of Daughter isotopes is the
isochron equation
