HOW C-14 DATING WORKS! (SHORT VIDEO FOR BETTER UNDERSTANDING)

C-14, or Carbon-14 is one of the popular radioactive elements used for "dating" aged artifacts/rocks/fossils that was dug out from an archaeologic site. As long as the object got Carbon, we could use C-14 to date how old the object is.

Here is a video that  explains how C-14 and the use of its HALF-LIFE works for us.

 

Courtesy: www.youtube.com

SAMPLE PROBLEM (FOR BETTER UNDERSTANDING)

1. Consider strontium-90 which has a half-life of approximately 28 years.
   • Initially, at time t=0, the sample is 100% strontium-90
   • After 28 years, only half the original amount of strontium will remain:
         ½ x 100% = 50%
   • After another 28 years, only half of this amount of strontium-90 will remain:
         ½ x 50% = 25%
   • After another 28 years, only half of this amount of strontium will remain:
         ½ x 25% = 12.5%
   • and so on.
   • At any given time,
         the amount of strontium-90 that has undergone decay can be calculated:     amount of strontium-90 decayed = the original amount - the amount remaining.
   
   

   Number of Half-lives Time (years) % Strontium-90 remaining % Strontium-90 that has decayed 0 0 100 0 1 28 50 50 2 56 25 75 3 84 12.5 87.5 4 112 6.25 93.75 5 140 3.125 96.875 6 168 1.5625 98.4375

2.  Calculate the percentage of strontium-90 remaining after 280 years.
3. N_t = N_o x (0.5)^{number of half-lives}
   N_t = ? %
   N_o = 100%
   number of half-lives = time ÷ half-life = 280 ÷ 28 =10
   N_t = 100 x (0.5)¹⁰ = 0.098%
   
   Reference: (http://www.ausetute.com.au/halflife.html)

THE FORMULA OF HALF-LIFE

The amount of radioactive isotope remaining can be calculated:

   

N_t = N_o x (0.5)^{number of half-lives}

    Where:
    N_t = amount of radioisotope remaining
    N_o = original amount of radioisotope
    number of half-lives = time ÷ half-life

HOW DO GEOLOGIST USE HALF-LIFE TO DATE ROCKS?

Geologic Dating

1. Geologists are always interested in the exact age of the rock and mineral samples which they are working with. While there are several different methods of determining a rock's age (such as examining the layer it is found in), the most reliable measure currently available to geologists is measuring the radioactive decay in isotopes found in a rock. This is referred to as "dating" a rock by the half-life of its isotopes. However, this process can be much more difficult than most people think it is.

Isotopes and Radioactive Decay

2. An isotope is an atom of a chemical element whose nucleus has the same atomic number but which has a different atomic weight. What this means is that an isotope can be thought of as a different version of a standard element on the periodic table. Due to its difference though, isotopes are atomically unstable, and prone to change into other, more stable elements. This process is referred to as radioactive decay. The rate at which radioactive decay occurs is that particular isotope's half-life. Just what all of that means is simple--once you get past the scientific terminology.

Measurement

3. The half-life of an isotope is how long it will take for half of the atoms present to decay and form another, more stable element. For instance, if there are 100 atoms of an isotope with a half-life of 20 years, then in 20 years there will be 50 atoms of it left. In another 20 years, there will be 25 atoms of it, and so on. This is an important process for geologists. If they find an isotope in a rock, along with all the atoms of the element the isotope decays into, then they can figure out how much of the original isotope has decayed. If they also know the rate of that decay, or the half-life, then they can determine how long this process took, and thus figure out the age of the rock. 

Reference: (http://www.ehow.com/how-does_5494507_do-use-halflife-date-rocks.html)

HALF-LIFE IMGS. (FOR BETTER UNDERSTANDING)

 

Image 1 shows the Radioactive decay of C-14 (used in Carbon Dating). The image/graph denotes that the fraction of the element C-14 is INVERSELY PROPORTIONAL to the number of half-lives it underwent.

 

Image 2 shows how the undecayed element were "half-ed"/decreased as half-life occurs, hence the name "half-life". In every half-life of the element, the undecayed atom would decrease by half and after, by half and so on...

LIST OF THE HALF-LIVES OF COMMONLY ENCOUNTERED RADIONUCLIDES

Element	Isotopes w/ Half life
Actinium	Ac-225 - 10.0 days Ac-227 - 21.773 years Ac-228 - 6.13 hours
Americium	Am-241 - 432.2 years Am-242 - 16.02 hours Am-242m - 152 years Am-243 - 7380 years
Antimony	Sb-124 - 60.20 days Sb-125 - 2.77 years Sb-126 - 12.4 days Sb-126m - 19.0 minutes Sb-127 - 3.85 days
Argon	Ar-41 - 1.827 hours
Astatine	At-217 - 0.0323 seconds At-218 - 2 seconds
Barium	Ba-137m - 2.552 minutes Ba-139 - 82.7 minutes Ba-140 - 12.74 days Ba-141 - 18.27 minutes Ba-142 - 10.6 minutes
Beryllium	Be-10 - 1.6E6 years Be-7 - 53.44 days
Bismuth	Bi-210 - 5.012 days Bi-211 - 2.14 minutes Bi-212 - 60.55 minutes Bi-213 - 45.65 minutes Bi-214 - 19.9 minutes
Bromine	Br-82 - 35.30 hours Br-83 - 2.39 hours Br-84 - 31.80 minutes
Cadmium	Cd-113m - 13.6 years Cd-115m - 44.6 days
Calcium	Ca-41 - 1.3E5 years Ca-47 - 4.53 days
Californium	Cf-252 - 2.638 years
Carbon	C-11 - 20.38 minutes C-14 - 5730 years
Cerium	Ce-141 - 32.50 days Ce-143 - 33.0 hours Ce-144 - 284.3 days
Cesium	Cs-134 - 2.062 years Cs-134m - 2.90 hours Cs-135 - 2.3E6 years Cs-136 - 13.1 days Cs-137 - 30.0 years Cs-138 - 32.2 minutes
Chromium	Cr-51 - 27.704 days
Cobalt	Co-56 - 78.76 days Co-57 - 270.9 days Co-58 - 70.8 days Co-60 - 5.27 years
Copper	Cu-61 - 3.408 hours Cu-64 - 12.701 hours
Curium	Cm-242 - 162.8 days Cm-243 - 28.5 years Cm-244 - 18.11 years Cm-245 - 8500 years Cm-246 - 4730 years Cm-247 - 1.56E7 years Cm-248 - 3.39E5 years
Europium	Eu-152 - 13.33 years Eu-154 - 8.8 years Eu-155 - 4.96 years Eu-156 - 15.19 days
Fluorine	F-18 - 109.74 minutes
Francium	Fr-221 - 4.8 minutes Fr-223 - 21.8 minutes
Gadolinium	Gd-152 - 1.08E14 years
Gallium	Ga-67 - 3.261 days
Gold	Au-198 - 2.696 days
Holmium	Ho-166m - 1.20E3 years
Hydrogen	H-3 - 12.35 years
Indium	In-111 - 2.83 days In-113 - 1.658 hours In-115 - 5.1E15 years
Iodine	I-123 - 13.2 hours I-125 - 60.14 days I-129 - 1.57E7 years I-130 - 12.36 hours I-131 - 8.04 days I-132 - 2.30 hours I-133 - 20.8 hours I-134 - 52.6 minutes I-135 - 6.61 hours
Iridium	Ir-192 - 74.02 days
Iron	Fe-55 - 2.7 years Fe-59 - 44.53 days
Krypton	Kr-83m - 1.83 hours Kr-85 - 10.72 years Kr-85m - 4.48 hours Kr-87 - 76.3 minutes Kr-88 - 2.84 minutes
Lanthanum	La-140 - 40.272 hours La-141 - 3.93 hours La-142 - 92.5 minutes
Lead	Pb-209 - 3.253 hours Pb-210 - 22.3 years Pb-211 - 36.1 minutes Pb-212 - 10.64 hours Pb-214 - 26.8 minutes Pb-214 - 26.8 minutes
Manganese	Mn-52 - 5.591 days Mn-52m - 21.1 minutes Mn-54 - 312.5 days Mn-56 - 2.579 hours Mn-57 - 36.08 hours
Mercury	Hg-197 - 64.1 hours Hg-203 - 46.60 days
Molybdenum	Mo-93 - 3.5E3 years Mo-99 - 66.0 hours
Neodymium	Nd-147 - 10.98 days
Neptunium	Np-237 - 2.14E6 years Np-238 - 2.117 days Np-239 - 2.355 days Np-240 - 65 minutes Np-240m - 7.4 minutes
Nickel	Ni-59 - 7.5E4 years Ni-63 - 96 years Ni-65 - 2.520 hours
Niobium	Nb-93m - 13.6 years Nb-95 - 35.15 days Nb-95m - 86.6 hours Nb-97 - 72.1 minutes Nb-97m - 60 seconds
Nitrogen	N-13 - 9.97 minutes N-16 - 7.13 seconds
Oxygen	O-15 - 122.24 seconds
Palladium	Pd-107 - 6.5E6 years Pd-109 0- 13.427 hours
Phosphorus	P-32 - 14.29 days
Plutonium	Pu-238 - 87.74 years Pu-239 - 24065 years Pu-240 - 6537 years Pu-241 - 14.4 years Pu-242 - 3.76E5 years Pu-243 - 4.956 hours Pu-244 - 8.26E7 years
Polonium	Po-210 - 138.38 days Po-211 - 0.516 seconds Po-212 - 0.305 microseconds Po-213 - 4.2 microseconds Po-214 - 164.3 microseconds Po-215 - 0.00178 seconds Po-216 - 0.15 seconds Po-218 - 3.05 minutes
Potassium	K-40 - 1.27E9 years K-42 - 12.36 hours K-43 - 22.6 hours
Praseodymium	Pr-143 - 13.56 days Pr-144 - 17.28 minutes Pr-144m - 7.2 minutes
Promethium	Pm-147 - 2.6234 years Pm-148 - 5.37 days Pm-148 - 41.3 days Pm-149 - 53.08 hours Pm-151 - 28.40 hours
Protactinium	Pa-231 - 3.28E4 years Pa-233 - 27.0 days Pa-234 - 6.70 hours Pa-234m - 1.17 minutes
Radium	Ra-223 - 11.434 days Ra-224 - 3.66 days Ra-225 - 14.8 days Ra-226 - 1600 years Ra-228 - 5.75 years
Radon	Rn-219 - 3.96 seconds Rn-220 - 55.6 seconds Rn-222 - 3.824 days
Rhenium	Re-187 - 5E10 years
Rhodium	Rh-103m - 56.12 minutes Rh-105 - 35.36 hours Rh-106 - 29.9 seconds
Rubidium	Rb-86 - 18.66 days Rb-87 - 4.7E10 years Rb-88 - 17.8 minutes Rb-89 - 15.2 minutes
Ruthenium	Ru-103 - 39.28 days Ru-105 - 4.44 hours Ru-106 - 368.2 days Ru-97 - 2.9 days
Samarium	Sm-147 - 1.06E11 years Sm-151 - 90 years Sm-153 - 46.7 hours
Scandium	Sc-44 - 3.927 hours Sc-46 - 83.83 days Sc-47 - 3.351 days Sc-48 - 43.7 hours
Selenium	Se-75 - 119.78 days Se-79 - 65000 years
Silver	Ag-110 - 24.6 seconds Ag-110m - 249.9 days Ag-111 - 7.45 days
Sodium	Na-22 - 2.602 years Na-24 - 15.00 hours
Strontium	Sr-85 - 64.84 days Sr-87m - 2.81 hours Sr-89 - 50.5 days Sr-90 - 29.12 years Sr-91 - 9.5 hours Sr-92 - 2.71 hours
Sulfur	S-35 - 87.44 days
Technetium	Tc-101 - 14.2 minutes Tc-99 - 2.13E5 years Tc-99m - 6.02 hours
Tellurium	Te-125m - 58 days Te-127 - 9.35 hours Te-127m - 109 days Te-129 - 69.6 minutes Te-129m - 33.6 days Te-131 - 25.0 minutes Te-131m - 30 hours Te-132 - 78.2 hours Te-133 - 12.45 minutes Te-133m - 55.4 minutes Te-134 - 41.8 minutes
Terbium	Tb-160 - 72.3 days
Thallium	Tl-201 - 73.06 hours Tl-207 - 4.77 minutes Tl-208 - 3.07 minutes Tl-209 - 2.20 minutes
Thorium	Th-227 - 18.718 days Th-228 - 1.913 years Th-229 - 7340 years Th-230 - 7.7E4 years Th-231 - 25.52 hours Th-232 - 1.41E10 years Th-234 - 24.10 days
Tin	Sn-119m - 293.1 days Sn-123 - 129.2 days Sn-125 - 9.64 days Sn-126 - 1.0E5 years
Tungsten	W-181 - 121.2 days W-185 - 75.1 days W-187 - 23.9 hours
Uranium	U-232 - 72 years U-233 - 1.59E5 years U-234 - 2.445E5 years U-235 - 7.03E8 years U-236 - 2.34E7 years U-237 - 6.75 days U-238 - 4.47E9 years U-240 - 14.1 hours
Vanadium	V-48 - 16.238 days
Xenon	Xe-131m - 11.9 days Xe-133 - 5.245 days Xe-133m - 2.188 days Xe-135 - 9.09 hours Xe-135m - 15.29 minutes Xe-138 - 14.17 minutes
Ytterbium	Yb-169 - 32.01 days
Yttrium	Y-90 - 64.0 hours Y-91 - 58.51 days Y-91m - 49.71 minutes Y-92 - 3.54 hours Y-93 - 10.1 hours
Zinc	Zn-65 - 243.9 days Zn-69 - 57 minutes
Zirconium	Zr-93 - 1.53E6 years Zr-95 - 63.98 days Zr-97 - 16.90 hours