Wednesday, December 14, 2011

Carbon Dating

നമ്മുടെ വായനക്കാരൊക്കെ രസതന്ത്രജ്ഞാന്മാരും ഊര്‍ജതന്ത്രജ്ഞാന്മാരും ഉണ്ടെന്നറിഞ്ഞതില്‍ സന്തോഷം. എനിക്കും കാര്‍ബണികരസതന്ത്രത്തില്‍ ( Organic Chemistry) ചെറിയ ഒരു ബിരുദാനന്തര ബിരുതം എടുക്കേണ്ട ഗതികേട് വന്നുഭവിച്ചു , വളരെ കുറച്ചു പ്രായോഗിക പരിജ്ഞാനവും ഉള്ളതുകൊണ്ട്. എനിക്കറിയാവുന്നത് ഞാന്‍ പറയട്ടെ. കാര്‍ബണ്‍ ഡേറ്റിങ്ങ് എങ്ങിനയോ അംഗീകാരം നേടിയെങ്കിലും , അതിനുപയോഗിക്കുന്ന അളവുകോലുകളെ പഠിച്ചിരുന്ന കാലത്തുതന്നെ എതിര്‍ത്തു , അദ്ധ്യാപകന്‍റെ കണ്ണിലെ കരടായി , ശിക്ഷയും ഏറ്റുവാങ്ങിയവനാണ് .

ഈ രീതിക്ക് വളരെയധികം പോരായ്മകളുണ്ട് . ഒന്ന് കാര്‍ബണിന്‍റെ ഒരയിസോട്ടോപ്പായ C14 radioactivedecay സംഭവിച്ചു നൈട്രജനായി n14 ആയി മാറുമ്പോള്‍ അതിന്‍റെ തോത് ഒരേ അളവിലാനെന്നു അനുമാനിച്ചാണ് ,കണക്കുകൂട്ടല്‍ , ( rate of decay can be affected a lot by various phisical factors like tem,pr,gravity,magnetic field,etc. and they are asuume that amount of C14 absorbtion is same since the time of earth created. എങ്ങിനെയാണ് C14 ഉണ്ടാകുന്നത് എന്ന് പോലും അനുമാനമാണ് ( സൂര്യനിലെയോ , മറ്റു നക്ഷത്രങ്ങളിലെയോ കോസ്മിക് രെശ്മികള്‍ അന്തരീക്ഷത്തിലെ നൈട്രജനെ n14 ഒരു പ്രോട്ടോണ്‍ എമിറ്റ് ചെയ്യിച്ചു C14 ആക്കുഉന്നൂ എന്നാണ് സിദ്ധാന്തം. അതുനടക്കുന്നതോ ഭൂമിയില്‍നിന്നും 15 മയില്‍ മുകളില്‍ വച്ചാണെന്നും പറയുന്നൂ. എന്ത് ചെയ്യാം ഇതൊക്കെ നമ്മള്‍ കണ്ണടച്ച് വിശ്വസിക്കുക .( Carbon-14 is produced in the atmosphere when neutrons from cosmic radiation react with nitrogen atoms: 147N + 10n → 146C + 11H) . ഈ കാര്‍ബണ്‍ ഓക്സിജനുമായി ചേര്‍ന്ന് കാര്‍ബണ്‍ ഡയോക്സയിട് രൂപപ്പെടുന്നൂ . ഇത് പ്രകാശസംശ്ലേഷണംവഴി ചെടികളില്‍ എത്തുന്നൂ , അവിടെനിന്നും ,ജീവികളിലും ,ഇവയില്‍നിന്നും മനുഷ്യനിലുംഎത്തുന്നൂ. ചാകുമ്പോള്‍ C14 :C12 അനുപാതം എല്ലാത്തിലും ഒന്നായിരിക്കുമെന്നും(അത് ചോദ്യം ചെയ്യാന്‍ പാടില്ല), ‍മൊത്തമുള്ള C14 തിരിച്ചു 147N ആകുന്നതു ഓരെവേഗത്തിലായിരിക്കുമെന്നും അനുമാനിക്കുന്നൂ. ( ഉധാഹരനത്തിനു ഒരു നിശ്ചിത ഭാഗത്ത് നിന്നും പത്തു ഗ്രാം C14 അഞ്ചു ഗ്രാം C14 നും അഞ്ചു ഗ്രാം N14 ആകണമെങ്കില്‍ 5730 വര്‍ഷം വേണമെന്ന് ചുരുക്കം. അത് രണ്ടര ഗ്രാമേ ഉള്ളൂഎങ്കില്‍ 11460 വര്‍ഷം പ്രായം. ഒന്നേകാല്‍ ഗ്രാമേയുള്ളൂ എങ്കില്‍ 22920 വര്‍ഷം പ്രായം. എന്തൊരു കണക്കു. ഇതുവച്ച് ഭൂമിക്കു അനേക കോടി വര്‍ഷങ്ങളുടെ പ്രായം , ബൈബിള്‍ പറയുന്നത് ജീവികളെ ഉണ്ടായിട്ടു 10000 വര്‍ഷത്തില്‍ താഴെ .

Accuracy of carbon dating?

I've been doing a some research on archaeology and some recent digs. Then I came across an article which stated in part:

The unreliability of carbon 14 date testing is a great concern to honest archaeologists. They get very concerned when C14 testing shows obviously inaccurate results & they are left in uncertainty about the reliability of the dates that they have previously never questioned.

Examples of abnormal C14 results include testing of recently harvested, live mollusc shells from the Hawaiian coast that showed that they had died 2000 years ago and snail shells just killed in Nevada, USA, dated in at 27,000 years old. A freshly killed seal at McMurdo Sound, Antarctica, yielded a death age of 1300 years ago.

A petrified miner’s hat & wooden fence posts were unearthed from an abandoned 19th century gold hunter’s town in Australia's outback. Results from radiocarbon dating said that they were 6000 years old.

Should carbon dating be trusted? Is there something better?
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Radio-carbon dating is a method of obtaining age estimates on organic materials. The word "estimates" is used because there is a significant amount of uncertainty in these measurements. Each sample type has specific problems associated with its use for dating purposes, including contamination and special environmental effects. More information on the sources of error in carbon dating are presented at the bottom of this page.
The method was developed immediately following World War II by Willard F. Libby and coworkers and has provided age determinations in archeology, geology, geophysics, and other branches of science. Radiocarbon dating estimates can be obtained on wood, charcoal, marine and freshwater shells, bone and antler, and peat and organic-bearing sediments. They can also be obtained from carbonate deposits such as tufa, calcite, marl, dissolved carbon dioxide, and carbonates in ocean, lake and groundwater sources.
Carbon dioxide is distributed on a worldwide basis into various atmospheric, biospheric, and hydrospheric reservoirs on a time scale much shorter than its half-life. Measurements have shown that in recent history, radiocarbon levels have remained relatively constant in most of the biosphere due to the metabolic processes in living organisms and the relatively rapid turnover of carbonates in surface ocean waters.However, changes in the atmosphere over the ages are a source of uncertainty in the measurements.
Carbon (C) has three naturally occurring isotopes. Both C-12 and C-13 are stable, but C-14 decays by very weak beta decay to nitrogen-14 with a half-life of approximately 5,730 years. Naturally occurring radiocarbon is produced as a secondary effect of cosmic-ray bombardment of the upper atmosphere. Plants transpire to take in atmospheric carbon, which is the beginning of absorption of carbon into the food chain. Animals eat the plants and this action introduces carbon into their bodies.
After the organism dies, carbon-14 continues to decay without being replaced. To measure the amount of radiocarbon left in a artifact, scientists burn a small piece to convert it into carbon dioxide gas. Radiation counters are used to detect the electrons given off by decaying C-14 as it turns into nitrogen. The amount of C-14 is compared to the amount of C-12, the stable form of carbon, to determine how much radiocarbon has decayed, thereby dating the artifact.
Exponential Decay Formula: A = A0* 2^(-t/k)
Where "A" is the present amount of the radioactive isotope, "A0" is the original amount of the radioactive isotope that is measured in the same units as "A." The value "t" is the time it takes to reduce the original amount of the isotope to the present amount, and "k" is the half-life of the isotope, measured in the same units as "t."
The applet allows you to choose the C-14 to C-12 ratio, then calculates the age of our skull from the formula above.
Uncertainty in Carbon DatingAs mentioned above, there is significant uncertainty in carbon dating. There are several variables that contribute to this uncertainty. First, as mentioned previously, the proportions of C-14 in the atmosphere in historic times is unknown. The C-14:C-12 atmospheric ratio is known to vary over time and it is not at all certain that the curve is “well behaved.”
Complicating things further, various plants have differing abilities to exclude significant proportions of the C-14 in their intake. This varies with environmental conditions as well. The varying rates at which C-14 is excluded in plants also means that the apparent age of a living animal may be affected by an animal's diet. An animal that ingested plants with relatively low C-14 proportions would be dated older than their true age.
Attempts are often made to index C-14 proportions using samples of know age. While this may be useful to eliminate the uncertainty of atmospheric proportions of C-14, it does not compensate for local conditions such as which plant species are in the diet. The uncertainty in the measurement leads some to conclude that the method is far less predictive of age than is commonly supposed, especially for older samples


146C → 147N + 0-1e (half-life is 5720 years)
Example Problem
A scrap of paper taken from the Dead Sea Scrolls was found to have a 14C/12C ratio of 0.795 times that found in plants living today. Estimate the age of the scroll.
Solution
The half-life of carbon-14 is known to be 5720 years. Radioactive decay is a first order rate process, which means the reaction proceeds according to the following equation:
log10 X0/X = kt / 2.30
where X0 is the quantity of radioactive material at time zero, X is the amount remaining after time t, and k is the first order rate constant, which is a characteristic of the isotope undergoing decay. Decay rates are usually expressed in terms of their half-life instead of the first order rate constant, where
k = 0.693 / t1/2
so for this problem:
k = 0.693 / 5720 years = 1.21 x 10-4/year
log X0 / X = [(1.21 x 10-4/year] x t] / 2.30
X = 0.795 X0, so log X0 / X = log 1.000/0.795 = log 1.26 = 0.100
therefore, 0.100 = [(1.21 x 10-4/year) x t] / 2.30
t = 1900 years


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