2 - introduction to isotopes and what they are

Question 1

isotopes

Answer 1

atoms of the same element that vary in mass due to different number of neutrons
(horizontal)

Question 2

isobar

Answer 2

atoms of different elements with different no. protons and neutrons but the same overall mass balance (diagonal?)

Question 3

isotone

Answer 3

atoms of different elements, different protons and neutrons (vertical)

Question 4

becoming neutron heavy means

Answer 4

increasing autonomic number (right of the line)

Question 5

what elements are radioactive

Answer 5

most elements are not
only certain elements isotopes
253/288 natural isotopes so no evidence of radioactive decay

Question 6

60% of natural isotopes have..

Answer 6

.. Even number of protons and/or neutrons

in general are the most abundant isotopes on earth

Question 7

40% of natural isotopes have…

Answer 7

… even number of protons and odd number of neutrons

… odd number of protons and even number of neutrons

Question 8

4 stable nuclei

Answer 8

odd number of protons and neutrons - all with relatively low numbers:
(2/1)H, (6/3)Li, (10/5)B, (14/7)N

Question 9

elements with an ??? Z have more stable isotopes

Answer 9

EVEN

Question 10

area of stability

Answer 10

plot A against Z for all known nuclei

Question 11

Z/N ratio gradually ???? until element ??

Answer 11

decreases

83 (Bi, the last on with a stable isotope)

Question 12

at high Z stability of a nuclide is favored by being …

Answer 12

… neutron rich

Question 13

stability of a nuclide is favored by …

Answer 13

… even number of protons and neutrons but not usually equal numbers

Question 14

coulombrepulsion

Answer 14

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

Question 15

strong nuclear force

Answer 15

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

Question 16

the shell model

Answer 16

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

Question 17

radio activity - Alpha (a) decay

Answer 17

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

Question 18

Radio activity - B decay

Answer 18

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 (?)

Question 19

Radio activity - electron capture

Answer 19

proton (from parent) dissociated/loses/ejects a proton
proton changes to a neutron
-1Z, +1N
potassium Aragon dating

down right decay scheme (?)

Question 20

valley of stability

Answer 20

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

Question 21

1902 Rutherford and saddy

Answer 21

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

Question 22

isochron equation

Answer 22

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

Question 23

two basic assumptions made when using radioactive decay and isochron equation to date rocks

Answer 23

1. the decay constant for the element is known

2. the decay constant for the element has not changed over time

Question 24

methods for determining the decay constant of an unstable isotope

Answer 24

• direct counting g
• daughter isotope measurement
• geological comparison

Question 25

direct counting method (method for determining decay constant of an unstable isotope)

Answer 25

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

Question 26

daughter isotope method (method for determining decay constant of an unstable isotope)

Answer 26

(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)

Question 27

geological comparison (method for determining decay constant of an unstable isotope)

Answer 27

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.

Question 28

demonstrating the decay constant for the element has not changed over time, several ways

Answer 28

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

Question 29

The Oklo natural nuclear reactor

Answer 29

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).

Question 30

decay is a …

Answer 30

purely random process

Question 31

radioactivity is a …

Answer 31

one way street, can’t convert back to parent

Question 32

precision

Answer 32

how close a series of measurements are to one another

Question 33

accuracy

Answer 33

how close a series of measurements are to the true/known/accepted value

need standards to prove the accuracy of labs

Question 34

Radioactive decay is constant:

Answer 34

• rate given by decay constant Lamda,
  or
• by time it takes for half the parent isotope to decay to the daughter isotope: (half-life)

Question 35

Equation defining decay of Parent and production of Daughter isotopes is the

Answer 35

isochron equation