Age of earth or mineral
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Age of earth or mineral-
Uranium – Lead dating method is used to determine the age of earth or a mineral. One gram atom of U238 disintegrates to give one gram atom of Pb 206. Gram atoms of U238 and Pb 206 are determined in the given sample. To use the following formula , it is assumed that no lead was present originally in the mineral-
K = (2.303 / t) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]
t = (2.303 / K) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]
t = Age of earth or mineral
Question 1) A sample of U – 238 is found to contain 23.8 gm of U – 238 and 20.6 gm Pb- 206. Calculate the age of uranium ore. t1/2 for uranium is 4.5 x 109 years.
Solution )
Half life of uranium (t1/2) = 4.5 x 109 years
K = 0.693 / t1/2 = 0.693 / 4.5 x 109
K = 0.154 x 10-9 = 1.54 x 10-10 years-1
Weight of uranium = 23.8 gm
Gram atoms of U 238 = w/m = 23.8 / 238 = 0.1
Gram atoms of Pb 206 =w/m = 20.6 / 206 = 0.1
t = (2.303 / K) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]
= (2.303 / 1.54 x 10-10 ) [log (0.1 + 0.1)/ 0.1]
= 1.495 x 1010( log 2)
Because ,log 2 = 0.3010
= 1.495 x 1010 x 0.3010 = 0.4499 x 1010
t = 4.5 x 109 years
Question 2) 92 U 238 disintegrates to give 82 Pb 206. A sample of uranium contains 1.0 gram of U 238 and 0.1 gram of Pb 206. Half life of uranium is 4.5 x 109 years . Calculate the age of uranium sample?
Solution )
Half life of uranium (t1/2) = 4.5 x 109 years
K = 0.693 / t1/2 = 0.693 / 4.5 x 109
K = 0.154 x 10-9 = 1.54 x 10-10 years-1
Weight of uranium = 1.0 gm
Gram atoms of U 238 = w/m = 1.0 / 238 = 0.0042
Gram atoms of Pb 206 =w/m = 0.1 / 206 = 0.000485
t = (2.303 / K) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]
= (2.303 / 1.54 x 10-10 ) [log (0.0042 + 0.000485)/ 0.0042]
= 1.495 x 1010[log ( 0.004685)/ 0.0042]
= 1.495 x 1010( log 1.1154)
Because ,log 1.1154 = 0.0474
= 1.495 x 1010 x 0.0474 = 0.0708 x 1010
t = 7.08 x 108 years
Question 3) On analysis a sample of uranium ore was found to contain 0.277 gm of 82 Pb206 and 1.667 gm of 92U 238. The half life period of U238 is 4.51 x 109 years. If all the lead was assumed to have come from decay of 92 U 238, What is the age of earth?
Solution )
Let , age of earth = t years
Weight of uranium = 1.667 gm
Gram atoms of U 238 = w/m = 1.667 / 238 = 0.0070
Gram atoms of Pb 206 =w/m = 0.277 / 206 = 0.001345
half life of uranium (t1/2) = 4.51 x 109 years
K = 0.693 / t1/2 = 0.693 / 4.51 x 109
K = 0.154 x 10-9 = 1.54 x 10-10 years -1
t = (2.303 / K) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]
= (2.303 / 1.54 x 10-10 ) [log (0.0070 + 0.001345)/ 0.0070]
= 1.495 x 1010 [log ( 0.00835)/ 0.0070]
= 1.495 x 1010( log 1.192)
Because , log 1.192 = 0.07658
t = 1.495 x 1010 x 0.07658 = 0.1144 x 1010
Age of earth ‘t ‘= 1.144 x 109 years
