Dr. David Helfand is a Professor of Astronomy at Columbia University and Board Chair of the American Institute of Physics. AAA was incredibly fortunate to have him kick off our annual lecture series, in which a new lecture is presented on the second Tuesday of each month, from October through May. Check out the AAA Event Calendar for information about upcoming lectures and other exciting opportunities! What follows is an overview of Dr. Helfand’s fascinating lecture, summarized by our very own David Kiefer. Enjoy!
The central theme of Dr. Helfand’s talk was that the decay of radioactive isotopes allows atoms to act as historians, establishing timelines for events. Each of the 94 naturally existing elements consist of nearly identical atoms that exist in slightly different weights. All atoms of a given element must have the same number of protons in their nuclei, but they can have a different number of neutrons, giving them slightly different masses. These are called isotopes. Some isotopes are radioactive, meaning they spontaneously change into another atom. In other words, one element transforms into another element. The time it takes for half of a particular isotope to “decay” is its half-life (t1/2). These half-lives vary enormously.
- The shortest-lived atom is hydrogen-7 [1H7] a rare, artificial isotope with 1 proton and 6 neutrons. Its t1/2 = 2.3 x 10-23 s.
- The longest-lived atom is tellurium-128 [52Te128], an almost completely stable isotope with 52 protons and 76 neutrons. Its t1/2 = 2.2 x 1024 years, vastly longer than the age of the universe.
Mathematics Involving Half-Life
After any interval of time (t), the number of atoms of any isotope remaining in a sample (Nt) that started with (N0) atoms is given by Nt = N0 x 0.5^(t/ t1/2), where ^ designates an exponent. For example, a sample containing 1200 radioactive atoms having a half-life of 5 minutes will have only 75 left after 20 minutes. The other 1125 atoms will have changed into a different kind of atom:
Nt = 1200 x 0.5^(20 min/5 min) = 1200 x 0.5^4 = 1200 x 0.54 = 75 atoms
The time interval for an event or production of a new isotope can be determined from:
- The amount of a radioactive element remaining in a sample, or
- The amount of the new element produced, or
- A ratio of both these measurements.
First, a Review
Dr. Helfand began with a review. Matter is composed of molecules, which consists of atoms. The nuclei of all atoms contain protons and neutrons, which are formed from quarks that have the fractional electric charges of +2/3 and -1/3. Ultimately, all matter is formed from quarks, leptons (such as electrons), and bosons (which are particles that convey the forces of nature). They are essential in understanding why and how atoms spontaneously change. The present model of matter is the most exact and comprehensive of all models humans have devised.
These are some radioactive isotopes used in medicine, archeology, and astronomy:
|Time Interval||Useful Isotopes||Range of Their Half-Lives|
|Minutes to days||F-18, I-131, Tc-99, Fe-54, Co-68||108 min to 5.3 y|
|Years, decades, millennia||H-3, Sr-90, C-14||12.3 y to 5730 y|
|Geologic timescales||U-235, U-238, Th-232||704 My to 14 Gy|
|Cosmic timescales||Re-187, Rb-87||43 to 49 Gy|
The rest of the talk gave illustrations about how radioactive isotopes have been used.
Is This Wine Really Vintage From 1932?
Before 1950-1963 the isotope H-3 (“tritium”) was barely present in matter. The nuclear bombs being tested in the atmosphere during those years produced copious amounts of 1H3. Therefore, if a wine contains any H-3 it cannot come from 1932. In fact, the amount of H-3 in a wine can be used to determine the actual year the grapes were grown using H-3’s half-life and the remaining percent of isotope. The amount of H-3 in the wine is compared to the percentage of H-3 in the air when the isotope was first emitted by the nuclear tests.
The Diffusion of Maize From Mexico to New England
It’s possible to trace the way native tribes spread corn from Mexico to New England over the span of a few thousand years. Corn uses C-4 photosynthesis pathway – in other words, 4 carbon atoms begin the photosynthesis chemical reactions. More ancient foods from shrubs and trees use a C-3 pathway. This influences the uptake rate of carbon as the plants grow. Air has a natural C-13:C-12 ratio of -0.7%. In the faster reactions in C-3 pathway plants, the C-13 isotope is assimilated at a slower rate than C-12 because it’s slightly heavier and moves more slowly. This leads to a C-13:C-12 ratio of -2.85% in C-3 pathway plants. But in the slower reactions in C-4 pathway plants, C-13 is assimilated better since its weight is not as much of an impediment, comparatively. As a result, C-4 plants have a higher C-13:C-12 ratio of -1.25%. (The negative % derives from the definition of the scale so less negative means higher ratio of C-13.) Therefore, the C-13:C-12 ratio found in vegetable remains and the bones of native people over time can be used to trace the spread of corn northwards from Mexico to New England.
Interestingly, the timeline for dating the increasing ratio as corn spread northwards is obtained using another carbon isotope, Carbon-14. C-14 is radioactive and is produced at a fixed percentage in the upper atmosphere by high energy particles from the Sun and the galaxy beyond. Comparing the percentage of C-14 in organic artifacts (bones, leather, wood) to the constant percentage in the air when their material was growing determines when the artifacts were alive and manufactured. This is a widely used technique in archeology called “carbon-14 dating”. It is accurate to a few decades, even for materials produced several tens of thousands of years ago.
A plot of C-13/C-12 ratios against time (obtained from C-14 data) shows a rapid increase in the Midwest about 1500 years ago. That’s when native tribes planting corn and all other C-4 pathway crops propagated them northwards.
Dendrochronology: Tracing Events and Conditions Using Tree Rings
Tree rings reveal the age of a tree, as well as the temperature and humidity fluctuations as a tree grows. The standard method is to count the rings and measure their thickness and distances apart, say, in millimeters. Using these measurements, we can trace changes in climate and local weather for hundreds, even thousands, of years. Now enter isotopic analysis. Exact isotope ratios within individual rings can provide climate information to greater precision. The O-18:O-16 isotope ratio indicates the average temperature for each year of growth. This is because the heavier C-18 atoms are assimilated less easily than the lighter C-16 atoms in cooler temperatures. But that’s not all. The C-13:C-12 ratio can tell us about humidity, because the stomata openings on tree leaves change their rate of uptake of carbon dioxide according to the humidity. The rate of C-13 uptake will be measurably different depending on the humidity because it’s slightly heavier than C-12.
Variations in global temperatures over 2000 years have been traced using these isotopes. The change is only between +1°C and -1°C from the average temperature. However, even a small change of 0.3°C impacts local climate, weather, vegetation, and living conditions significantly. It led to migrations, extinctions, starvation, and changes in agriculture and animal husbandry. All this has been revealed by tree rings and the isotopes embedded in them.
In fact, by comparing temperature fluctuations collected from tree ring analysis with the timeline obtained from the C-14 dating of each ring, it’s possible to show that the Sun itself has fluctuated in its energy output. This is because solar energy determines the percentage of C-14 created by nuclear changes to oxygen and nitrogen in the upper atmosphere. Significant differences between the age determined from C-14 versus the age determined from tree rings can be explained by variations in the solar-constant, which is the total energy per second received by Earth from the Sun. Such variations do occur over thousands of years, each one lasting a few hundred years.
The Rapid Extinction of Dinosaurs
Paleontologists have long known that the dinosaurs died out rapidly. At a certain boundary between strata their bones are not present. What caused this rapid mass extinction was once a mystery. But the mystery’s been solved… by geologic, astronomic, and isotopic evidence. It was a 10 km meteor that slammed into Earth at the tip of Mexico’s Yucatan Peninsula (near Cancun) 66 million years ago. This is in agreement with dinosaur fossil records.
Meteors contain a higher percentage of the Ir-193 isotope of iridium than Earth’s crust. A thin boundary has been uncovered around the globe where the Ir-193 percentage jumps from 0.3 ppb (parts per billion) to 7 ppb. This is from the dust of the meteor that spread worldwide.
In addition, the impact formed vast amounts of zirconium crystals, ZrSiO4. This crystal is known for its ability to incorporate uranium (U) compounds but to reject lead (Pb) compounds. However, U atoms incorporated within zirconium slowly change into Pb atoms by radioactive decay. Therefore, the amount of Pb found in zirconium crystals at the worldwide boundary formed when the impact occurred can date the event, because those Pb atoms had to come from U atoms in the crystals— not by direct chemical incorporation of lead compounds.
A critique of this analysis was that the U compounds in the crystals could have leeched out, throwing off the U-to-Pb ratios within them. A more complex analysis was done based on two decays involving four isotopes.
U-235 → Pb-207
U-238 → Pb-206
The “daughter” to “parent” ratios in crystals are U-235:Pb-207 and U-238:Pb-206. This is known as establishing an “accumulation clock”. Graphical analysis of these ratios found in crystals can bypass the problem of the leeching of uranium from the crystals over time. This is known as a “concordia analysis”. This set the date of impact at 66 million years ago.
Further evidence for a meteor impact comes from the fact that the sulfuric acid (H2SO4) such an impact produces would have made the atmosphere reflect a lot of sunshine, thereby cooling the Earth. Estimates are that 3 gallons of sulfuric acid fell on each square meter, and that temperatures dropped from 20°C to -5°C within a week. Bad news for dinosaurs and for global photosynthesis initiating their food chain. The sulfuric acid dissolved many solids in the ground that flowed into the ocean. These materials included strontium compounds, containing Sr-86 and Sr-87 isotopes. The sulfuric acid would dissolve a greater percentage of Sr-87 compounds than rain water would, since this isotope is more common in land-based rocks than in seawater. Therefore, the ratio of Sr-87 to Sr-86 in seawater increased due to the acid’s effect. Indeed, analysis of the Sr-87:Sr-86 ratio in plankton and the remains of other organic life shows that the ratio dramatically popped-up 66 million years ago.
Add in a large underwater crater detected at the Yucatan tip. Add in fossils of fish found in the Gulf of Mexico located in Oklahoma that were carried by the tsunami from the impact. A meteor is to blame!
As he answered questions at the end of the lecture, Dr. Helfand made an amusing aside. This meteor probably struck in the third week of June of that year! This is evidenced by pollen and lines observed on fossilized leaves caused by their rapid freezing.
The Age of the Solar System
The rare isotope of strontium, Sr-87, can only be formed by the radioactive decay of the rubidium isotope, Rb-87.
37Rb87 → 38Sr87 + -1e0
[Beta emission: a neutron transforms into a proton and releases an electron.]
The half-life for this decay is enormous, t1/2 = 49 Gy = 49 billion years. One billion years after the Solar System formed the fraction of Rb-87 that remaining in it was:
Nt ÷ N0 = 0.5^(t/ t1/2) = 0.5^(1/49) = 0.50.0204 = .9860 or 98.60%
The missing 1.40% decayed into Sr-87. So 1 billion years after the Solar System formed it had a Sr-87:Rb-87 ratio = 1.40% ÷ 98.60% = 0.0142
Working in reverse, we can use the present Sr-87:Rb-87 found in rocks, the air, and meteorites to calculate the time that has passed since the Solar System formed. It turns out to be 4.56 ± 0.03 billon years.
Kilonovae are explosions 1000 times stronger than novae. A kilonova is believed to come from the collision and merging of two neutron stars which sends out gravitational waves through all space. Recent measurements of gravitational waves such as from LIGO have pinpointed coordinates in space where one of these mergers happened. Using telescopes, the event can be seen in visible and other electromagnetic waves. The flash seems to die out quickly from indicating a hot blue object to a cooler red object. Analysis of its light indicates a higher proportion of heavy elements like gold and platinum. This is the basis for a new theory that such heavy elements are produced mostly by neutron star mergers (kilonovae). This clears up the mystery of why the creation of sufficient gold and platinum could not be explained simply by nuclear reactions in supernovae.
Studies of the Interstellar Medium In Our Neck of the Woods in the Galaxy
The amazing Gaia satellite has tracked the Sun’s past and present movements through a unique bubble of gas in the Galaxy about 300 light-years wide during the past 100,000 years. There is evidence that a supernova occurred in this “small” bubble that affected the environment near the Sun and Solar System. German astrophysicists gathered a ton of snow from Antarctica to eventually obtain isotope ratios for Fe-60 and Mn-53 and also for Ni and Fe ratios. The data suggests such a supernova enriched these specific isotopes in the interstellar area near our Sun. What was remarkable is that they were able to determine that just 60 mg of Fe-60 fell per year on the entire Earth from this supernova.
Another Look at the Age of the Universe
The mass ratio of Helium to Hydrogen (He:H) in the Universe when it was 100 seconds old is roughly 0.25. This is obtained from spectra of the farthest, hence earliest, galaxies that formed out of this beginning H and He mixture. In addition, spectra of these earliest galaxies reveal their H-2:H-1 ratio was 0.000035 at 1 second. These ratios reflect transformations between protons and neutrons during those first 100 seconds.
From this data astrophysicists can determine temperature, composition, and density at 1 billionth of a second after the Big Bang, and that the age of the universe is 13.787 ± 0.020 billion years. This is consistent with prior determinations of the universe’s age, pinning it down to remarkable precision.
A final quote from Dr. Helfand captures the essence of his whole lecture: “Atoms are, truly, the universal historians.”