The Hydrogen isotope tritium, ^3_1 H, was discovered in 1932 and synthesized on

Question

The Hydrogen isotope tritium, ^3_1 H, was discovered in 1932 and synthesized on a large scale by Louis Alvarez et al in the late 1940's. If 200.00 mCi (milliCuries) of tritium synthesized on August 9.1950 were allowed to decay in a secure place until today, Aug 9, 2016 we would find only 4.795 mCi remaining. A) Based on this data what is the "half-life" of tritium? B) Starting from today how long would it take the above sample to further decay to 0.100 mCi? C) what was Louis Alvarez (and his son and two others) famous for in 1980? Look it up: Science. 208 (4448): 1095 - 1108, (1980)

Explanation / Answer

A)

from the data given

t = time = 66 years

a= initial amount = 200 mci

x = final amount = 4.795 mci

k = (1/t)ln(a/x)

   = (1/66)ln(200/4.795)

= 0.0565 y^-1

k = 0.693/t1/2

t1/2 = half life time = 0.693/0.0565

    = 12.265 years

B) a = 4.795 mci

    x = 0.1 mci

   t = ?

k = 0.565 year^-1

0.565 = (1/t)ln(4.795/0.1)

t = time required = 6.85 years

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