p44_031 - r = N 235 , /N 238 , (= 0 . 030). We solve for t...

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31. Let t be the present time and t = 0 be the time when the ratio of 235 Uto 238 Uwas3 . 0%. Let N 235 be the number of 235 U nuclei present in a sample now and N 235 , 0 be the number present at t =0.Let N 238 be the number of 238 U nuclei present in the sample now and N 238 , 0 be the number present at t =0 . The law of radioactive decay holds for each specie, so N 235 = N 235 , 0 e λ 235 t and N 238 = N 238 , 0 e λ 238 t . Dividing the Frst equation by the second, we obtain r = r 0 e ( λ 235 λ 238 ) t where r = N 235 /N 238 (= 0 .
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Unformatted text preview: r = N 235 , /N 238 , (= 0 . 030). We solve for t : t = 1 235 238 ln r r . Now we use 235 = (ln 2) /T 1 / 2 235 and 238 = (ln 2) /T 1 / 2 238 to obtain t = T 1 / 2 235 T 1 / 2 238 ( T 1 / 2 238 T 1 / 2 235 ) ln 2 ln r r = (7 . 10 8 y)(4 . 5 10 9 y) (4 . 5 10 9 y 7 . 10 8 y) ln 2 ln . 0072 . 030 = 1 . 71 10 9 y ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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