Radioisotopic Dating A

  
   
Professor W.F.Libby, Institute for Nuclear Studies in Chicago in 1947. Knew about C-14 production in atmosphere. Nobel Prize in Chemistry, 1960.
in stratosphere

Carbon-14 atoms are being continually created by cosmic rays, and continually destroyed by beta decay. The combination of these two processes means there is an equilibrium abundance of C-14 atoms of 1 in 1013. That is, 0.00000000001% of all carbon atoms are the carbon-14 isotope. These heavy carbon atoms form , which is absorbed by plants just like normal CO2.

Example: charcoal from Lascaux Cave in France has been found with . How old is it?

decay counter vs accelerator (mass spectrometer) dating
particle-track dating		 Activities & Practice
to do as you read
PROBLEMS
1. The half-life of for decay is 37.3 min. Given a 1.00-g sample at time zero, how long will it be before the sample is reduced to 0.25 g? What is the daughter nuclide?
2. Given that for is 10.1 min, what fraction of a given sample will be left after 1 hour?
3. A given sample of a radioactive isotope shows an activity of 8640 counts/min at one time, and 7620 counts/min 1 hour later. What is its half-life?
4. How do the particles ??????and ? differ from each other in charge and mass? Given a beam that consists of one of these particles, how could you tell experimentally which it is?
5. Among the fallout products from fission , which has a half-life for beta-decay of 28.1 yr. On the basis of its position in the periodic table, why might this fission product be a particularly dangerous one?
6. A wooden club found in a troglodyte cave shows a ratio which is 10% of the ratio shown by living trees today. How old is the club?
7. When a nuclear bomb is detonated, is most of the energy released (a) during the actual explosion, or (b) during the following weeks as the radioactive fallout decays?
8. Shown here is a schematic nuclide chart. The shaded region is the Belt of Stability. Two unspecified radioactive nuclides are at positions 1 and 2.
(a) What is the type of radioactivity most likely exhibited by nuclide 1?
(b) What is the type of radioactivity most likely exhibited by nuclide 2?
9. By weight, the human body has the following composition: O (65.0%), C (18.5%), H (9.5%), N (3.2%), Ca (1.5%), P (1.0%), K (0.4%), S (0.3%), Cl (0.2%), Na (0.2%), Mg (0.1%), and trace elements including Co, Cu, F, I, Fe, Mn, Zn totalling 0.1%. Based on your own body weight, determine how many carbon nuclei are in your body. Since one out of every 1013 carbon is the heavy C-14 nuclide, determine how many C-14 nuclei are in your body. How many disintegrate every minute?

9. Americium-241 decays by ?-decay. What is its daughter nuclide?
10. Carbon-14 (the nuclide that’s so useful in the dating of archaeological artifacts) decays by ?? emission, with a half-life of 5730 years. What is its daughter nuclide?
11. Strontium-92 forms as a result of the ?? decay of some another nuclide, its ‘parent’. What is the parent nuclide?
12. Below are shown the spectra of three stars, shown on the same axes for easy comparison. Which star is the hottest of the three?

13. The work function for aluminum is 4.2 eV. If light is shined onto an aluminum plate (inside a vacuum tube) and electrons with KE of 5.1 eV are detected, what is the energy (in eV) of the photons hitting the aluminum?
14. A streetlight is yellow. You are driving towards that stoplight very, very fast (i.e. fast enough for the Doppler Shift to be important.) Which one of the following colors could you not see, no matter how fast you go: blue, red, indigo, green?
15. Mercury-206 decays by ???emission, with a half-life of 450 seconds. If you had a kilogram of this stuff, how long would you have to wait for 7/8 of it to decay?
16. This cautionary Christmas tale is from New Statesman and Nation (London) 14 Jan 1950.
This is the Tale of Frederick Wermyss
Whose Parents weren’t on speaking terms.
So when Fred wrote to Santa Claus
It was in duplicate because
One went to Dad and one to Mum—
Both asked for some Plutonium.
See the result: Father and Mother—
Without Consulting one another—
Purchased two lumps of Largish Size,
Intending them as a Surprise,
Which met in Frederick’s Stocking and
Laid level Ten square miles of Land.

Explain what happened in Frederick’s stocking.

17. We discussed in the text one of the branches of the proton-proton chain, pp1. Here is another branch (called pp2), with some pieces missing from the equations. Fill in the blanks.

18. Radiocarbon dating can only be used to date archaeological objects that are younger than 70,000 years or so. Why can older objects not be dated using this technique?
19. Consider light shining on photographic film. The light will be recorded if it dissociates (splits) an AgBr molecule in the film. The minimum energy needed to do this is 1x10-19 J. What is the cutoff wavelength (in nm), greater than which light will not be recorded?
20. In the text we discussed uranium fission in atomic bombs. One way (after absorbing a neutron) can fission is into and , plus three neutrons. Some uranium nuclei don’t do this, but instead fission into antimony and niobium, plus some number of neutrons. How many neutrons are produced in this case?

21. Bones of the woolly mammoth have been found in North America. The youngest of these bones has a Carbon-14 activity 21% of what was present in the live animal. How long ago (in years) did this animal disappear from North America? ( ).
22. The third chain of the proton-proton cycle, pp3, is given here, with several reactants replaced with question marks. What are they?

23. The proton-proton chains are the dominant energy source for stars in a certain range of masses. Other stars use the CNO-cycle, so named because carbon, nitrogen, and oxygen act as intermediaries in the reactions, like catalysts. Here is the CNO cycle, with some reactants unspecified...

Notice that the net result is to convert four H's to one He, and the C, N, and O are left unchanged.
(a) Figure out the identities of the unnamed reactants.
(b) Based on the completed reaction formulas, would you expect the CNO cycle to be used by higher-mass stars, or lower-mass stars, compared to the proton-proton cycles? Explain your reasoning.
24. The Sun radiates energy into space at the rate of 3.90x1026W. How much does the mass of the Sun decrease every second as a result?
25. The energy released in the fission of a single U-235 nucleus is about 200 MeV. Calculate how high that amount of energy could cause a sand grain to jump. Take the sand grain to be cubical, 1 mm on a side, and having a density of 3 g/cm3.

  
   


 

 

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